Updated: July 5th, 2023 16:04

2018 journal article

Global attractors of some predator-prey reaction-diffusion systems with density-dependent diffusion and time-delays

*JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS*, *464*(1), 164–187.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

15. Life on Land
(OpenAlex)

Source: Web Of Science

Added: August 6, 2018

2017 journal article

Dynamics of degenerate quasilinear reaction diffusion systems with nonnegative initial functions

*JOURNAL OF DIFFERENTIAL EQUATIONS*, *263*(11), 7709–7752.

Source: Web Of Science

Added: August 6, 2018

2016 journal article

Dynamics of food-chain models with density-dependent diffusion and ratio-dependent reaction function

*JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS*, *433*(1), 355–374.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2016 journal article

Numerical methods for coupled systems of quasilinear elliptic equations with nonlinear boundary conditions

*Journal of Applied Analysis and Computation*, *6*(2), 543–581.

Source: NC State University Libraries

Added: August 6, 2018

2016 journal article

Numerical methods for fourth-order elliptic equations with nonlocal boundary conditions

*JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS*, *292*, 447–468.

author keywords: Fourth-order elliptic equation; Nonlocal boundary condition; Finite difference system; Method of upper and lower solutions; Monotone iterations; Convergence

TL;DR:
The monotone convergence property of the maximal and minimal sequences is used to show the convergence of themaximal and minimal finite difference solutions to the corresponding maximal and minimum solutions of the original continuous system as the mesh size tends to zero.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2015 journal article

Dynamics of Lotka-Volterra competition reaction-diffusion systems with degenerate diffusion

*JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS*, *421*(2), 1721–1742.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

15. Life on Land
(OpenAlex)

Source: Web Of Science

Added: August 6, 2018

2015 journal article

Dynamics of Lotka-Volterra cooperation systems governed by degenerate quasilinear reaction-diffusion equations

*NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS*, *23*, 47–60.

Source: Web Of Science

Added: August 6, 2018

2015 journal article

Existence and dynamics of quasilinear parabolic systems with time delays

*JOURNAL OF DIFFERENTIAL EQUATIONS*, *258*(9), 3248–3285.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2014 journal article

A Lotka-Volterra cooperating reaction-diffusion system with degenerate density-dependent diffusion

*NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS*, *95*, 460–467.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2013 journal article

Numerical methods for a coupled system of differential equations arising from a thermal ignition problem

*NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS*, *29*(1), 251–279.

UN Sustainable Development Goal Categories

13. Climate Action
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2013 journal article

On a coupled system of reaction-diffusion-transport equations arising from catalytic converter

*NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS*, *14*(6), 2152–2165.

UN Sustainable Development Goal Categories

13. Climate Action
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2013 journal article

Quasilinear parabolic and elliptic systems with mixed quasimonotone functions

*JOURNAL OF DIFFERENTIAL EQUATIONS*, *255*(7), 1515–1553.

UN Sustainable Development Goal Categories

15. Life on Land
(OpenAlex)

Source: Web Of Science

Added: August 6, 2018

2011 journal article

GLOBAL ATTRACTORS OF REACTION-DIFFUSION SYSTEMS MODELING FOOD CHAIN POPULATIONS WITH DELAYS

*COMMUNICATIONS ON PURE AND APPLIED ANALYSIS*, *10*(5), 1463–1478.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2010 journal article

BLOCK MONOTONE ITERATIVE METHOD FOR SEMILINEAR PARABOLIC EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

*SIAM JOURNAL ON NUMERICAL ANALYSIS*, *47*(6), 4581–4606.

author keywords: semilinear parabolic equations; nonlinear boundary conditions; finite difference systems; block monotone iterations; upper and lower solutions; Jacobi iterations and Gauss-Seidel iterations; numerical solutions; convergence

TL;DR:
It is shown that by using an upper solution and a lower solution as initial iterations each of the iterative schemes yields two sequences which converge monotonically from above and below, respectively, to a unique solution of the finite difference system.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2010 journal article

EIGENVALUE PROBLEMS OF A DEGENERATE QUASILINEAR ELLIPTIC EQUATION

*ROCKY MOUNTAIN JOURNAL OF MATHEMATICS*, *40*(1), 305–311.

Source: Web Of Science

Added: August 6, 2018

2010 journal article

Nonlinear fourth-order elliptic equations with nonlocal boundary conditions

*JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS*, *372*(2), 351–365.

Source: Web Of Science

Added: August 6, 2018

2010 journal article

Positive solutions of quasilinear parabolic systems with Dirichlet boundary condition

*JOURNAL OF DIFFERENTIAL EQUATIONS*, *248*(5), 1175–1211.

Source: Web Of Science

Added: August 6, 2018

2009 journal article

Singular reaction diffusion equations of porous medium type

*NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS*, *71*(5-6), 2033–2052.

Source: Web Of Science

Added: August 6, 2018

2008 journal article

Blowup and global existence of solutions for a catalytic converter in interphase heat-transfer

*Nonlinear Analysis. Real World Applications*, *9*(3), 822–829.

UN Sustainable Development Goal Categories

13. Climate Action
(Web of Science)

Source: NC State University Libraries

Added: August 6, 2018

2008 journal article

Numerical solutions of a three-competition Lotka-Volterra system

*APPLIED MATHEMATICS AND COMPUTATION*, *204*(1), 423–440.

author keywords: Lotka-Volterra competition; reaction-diffusion system; finite difference system; monotone iterative method; upper and lower solutions; asymptotic behavior

TL;DR:
Three monotone iterative schemes for the computation of the time-dependent solution are presented, and the sequences of iterations are shown to converge monotonically to a unique positive solution.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

15. Life on Land
(OpenAlex)

Source: Web Of Science

Added: August 6, 2018

2007 journal article

A Finite Difference Method and Analysis for 2D Nonlinear Poisson–Boltzmann Equations

*Journal of Scientific Computing*, *30*(1), 61–81.

author keywords: nonlinear Poisson-Boltzmann equation; exterior problem; immersed interface method; monotone iterative method

TL;DR:
A fast finite difference method based on the monotone iterative method and the fast Poisson solver on irregular domains for a 2D nonlinear Poisson–Boltzmann equation is proposed and analyzed and is efficient in terms of accuracy, speed, and flexibility in dealing with the geometry of the domain.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, Crossref

Added: August 6, 2018

2007 journal article

Monotone iterative methods for numerical solutions of nonlinear integro-elliptic boundary problems

*APPLIED MATHEMATICS AND COMPUTATION*, *186*(2), 1624–1642.

author keywords: integro-differential equations; reaction-diffusion-convection; finite-difference solution; monotone iterations; upper and lower solutions; existence-uniqueness theorem

TL;DR:
The aim of this paper is to obtain various monotone iterative schemes for numerical solutions of a class of nonlinear nonlocal reaction–diffusion–convection equations under linear boundary conditions.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2007 journal article

Numerical methods for quasi-linear elliptic equations with nonlinear boundary conditions

*SIAM JOURNAL ON NUMERICAL ANALYSIS*, *45*(3), 1081–1106.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2007 journal article

Positive solutions of quasilinear parabolic systems with nonlinear boundary conditions

*JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS*, *333*(1), 472–499.

Source: Web Of Science

Added: August 6, 2018

2007 journal article

Quasilinear parabolic and elliptic equations with nonlinear boundary conditions

*NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS*, *66*(3), 639–662.

Source: Web Of Science

Added: August 6, 2018

2007 journal article

The global attractor of a competitor-competitor-mutualist-reaction-diffusion system with time delays

*NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS*, *67*(9), 2623–2631.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2006 journal article

Time-delayed finite difference reaction-diffusion systems with nonquasimonotone functions

*NUMERISCHE MATHEMATIK*, *103*(3), 485–513.

author keywords: reaction-diffusion system; finite difference system; monotone iterative method; asymptotic behavior; local and global attractors

TL;DR:
The asymptotic behavior result leads to some local and global attractors of the time-dependent problem, including the convergence of theTime-dependent solution to a unique steady-state solution.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2005 journal article

Global attractor of coupled difference equations and applications to Lotka-Volterra systems

*ADVANCES IN DIFFERENCE EQUATIONS*, (1), 57–79.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2005 journal article

Stability and attractivity of periodic solutions of parabolic systems with time delays

*JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS*, *304*(2), 423–450.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2005 journal article

Strongly coupled elliptic systems and applications to Lotka-Volterra models with cross-diffusion

*NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS*, *60*(7), 1197–1217.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2004 journal article

Global asymptotic stability of Lotka-Volterra competition systems with diffusion and time delays

*NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS*, *5*(1), 91–104.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

15. Life on Land
(OpenAlex)

Source: Web Of Science

Added: August 6, 2018

2003 journal article

Accelerated monotone iterations for numerical solutions of nonlinear elliptic boundary value problems

*Computers & Mathematics With Applications*, *46*(37905), 1535–1544.

Source: NC State University Libraries

Added: August 6, 2018

2003 journal article

Block monotone iterations for numerical solutions of fourth-order nonlinear elliptic boundary value problems

*SIAM JOURNAL ON SCIENTIFIC COMPUTING*, *25*(1), 164–185.

author keywords: fourth-order elliptic equations; finite difference systems; block monotone iterations; numerical solutions; convergence; upper and lower solutions

TL;DR:
It is shown that the sequence of iterations converges monotonically to a maximal solution or a minimal solution if the nonlinear function is quasi-monotone nondecreasing and that the finite difference solution converges to the continuous solution as the mesh size tends to zero.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2003 article

Finite difference reaction-diffusion systems with coupled boundary conditions and time delays (vol 272, pg 407, 2002)

*Journal of Mathematical Analysis and Applications*, Vol. 288, p. 870.

Source: NC State University Libraries

Added: August 6, 2018

2003 journal article

Global asymptotic stability of Lotka-Volterra 3-species reaction-diffusion systems with time delays

*JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS*, *281*(1), 186–204.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

15. Life on Land
(OpenAlex)

Source: Web Of Science

Added: August 6, 2018

2003 journal article

Global attractor of a coupled finite difference reaction diffusion system with delays

*JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS*, *288*(1), 251–273.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

15. Life on Land
(OpenAlex)

Source: Web Of Science

Added: August 6, 2018

2002 journal article

Convergence of solutions of reaction-diffusion systems with time delays

*NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS*, *48*(3), 349–362.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2002 journal article

Finite difference reaction-diffusion systems with coupled boundary conditions and time delays

*JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS*, *272*(2), 407–434.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2002 journal article

Time delayed parabolic systems with coupled nonlinear boundary conditions

*PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY*, *130*(4), 1079–1086.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2001 journal article

Finite difference solutions of reaction diffusion equations with continuous time delays

*COMPUTERS & MATHEMATICS WITH APPLICATIONS*, *42*(3-5), 399–412.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2001 journal article

Numerical methods for fourth-order nonlinear elliptic boundary value problems

*NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS*, *17*(4), 347–368.

Source: Web Of Science

Added: August 6, 2018

2001 journal article

Numerical methods for nonlinear integro-parabolic equations of Fredholm type

*COMPUTERS & MATHEMATICS WITH APPLICATIONS*, *41*(7-8), 857–877.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2001 journal article

Numerical methods for time-periodic solutions of nonlinear parabolic boundary value problems

*SIAM JOURNAL ON NUMERICAL ANALYSIS*, *39*(2), 647–667.

author keywords: time-periodic solution; reaction-diffusion-convection equation; monotone iterations; finite difference equations; convergence; error estimates

TL;DR:
It is shown by the method of upper and lower solutions that the sequence of iterations from each of these iterative schemes converges monotonically to either a maximal periodic solutions or a minimal periodic solution depending on whether the initial iteration is an upper solution or a lower solution.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2001 journal article

Numerical solutions of reaction-diffusion equations with nonlocal boundary conditions

*JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS*, *136*(1-2), 227–243.

Source: Web Of Science

Added: August 6, 2018

2001 journal article

Quenching problem of a functional parabolic equation

*Journal of High Energy Physics*, *8*(1), 89–98.

Source: NC State University Libraries

Added: August 6, 2018

2001 article

Reaction diffusion systems with time delays in a half-space domain

Pao, C. V. (2001, August). *NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS*, Vol. 47, pp. 4365–4375.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2000 chapter

Dynamics of a Volterra-Lotka competition model with diffusion and time delays, integral and integro differential equations

In R. P. Agarwal & D. O'Regan (Eds.), *Integral and integrodifferential equations: Theory, method and applications (Series in mathematical analysis and applications ; v.2 )* (Vol. 2, pp. 269–277). Amsterdam: Gordon and Breach Science Publishers.

Ed(s): R. Agarwal & D. O'Regan

Source: NC State University Libraries

Added: August 6, 2018

2000 journal article

Finite difference reaction-diffusion equations with nonlinear diffusion coefficients

*NUMERISCHE MATHEMATIK*, *85*(3), 485–502.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2000 journal article

On fourth-order elliptic boundary value problems

*Proceedings of the American Mathematical Society*, *128*(4), 1023–1030.

Source: NC State University Libraries

Added: August 6, 2018

2000 journal article

Periodic solutions of parabolic systems with time delays

*JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS*, *251*(1), 251–263.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2000 journal article

Periodic solutions of systems of parabolic equations in unbounded domains

*NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS*, *40*(1-8), 523–535.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2000 journal article

Quenching problem of a reaction-diffusion equation with time delay

*NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS*, *41*(1-2), 133–142.

Source: Web Of Science

Added: August 6, 2018

1999 journal article

Numerical analysis of coupled systems of nonlinear parabolic equations

*SIAM JOURNAL ON NUMERICAL ANALYSIS*, *36*(2), 393–416.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

1999 journal article

Numerical methods for systems of nonlinear parabolic equations with time delays

*JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS*, *240*(1), 249–279.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

1999 journal article

Periodic solutions of parabolic systems with nonlinear boundary conditions

*JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS*, *234*(2), 695–716.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

1999 journal article

Positive solutions and dynamics of some reaction diffusion models in HIV transmission

*NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS*, *35*(3), 323–341.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science; OpenAlex)

Source: Web Of Science

Added: August 6, 2018

1998 journal article

Accelerated monotone iterative methods for finite difference equations of reaction-diffusion

*NUMERISCHE MATHEMATIK*, *79*(2), 261–281.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

1998 journal article

Asymptotic behavior of solutions of reaction-diffusion equations with nonlocal boundary conditions

*Journal of Computational and Applied Mathematics*, *88*(1998), 225–238.

Source: NC State University Libraries

Added: August 6, 2018

1998 journal article

Dynamics of a finite difference system of reaction diffusion equations with time delay

*JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS*, *4*(1), 1–11.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

1998 journal article

Monotone iterations for numerical solutions of reaction-diffusion-convection equations with time delay

*Numerical Methods for Partial Differential Equations*, *14*(3), 339–351.

Source: NC State University Libraries

Added: August 6, 2018

1998 journal article

Monotone methods for a finite difference system of reaction diffusion equation with time delay

*COMPUTERS & MATHEMATICS WITH APPLICATIONS*, *36*(10-12), 37–47.

author keywords: finite difference equations; reaction-diffusion; time delay; monotone iterations; upper and lower bounds

TL;DR:
The iterative schemes lead to computational algorithms as well as existence, uniqueness, and upper and lower bounds of the solution of a system of nonlinear difference equations with time delays.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

1998 journal article

Parabolic systems in unbounded domains I. Existence and dynamics

*JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS*, *217*(1), 129–160.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

1998 journal article

Parabolic systems in unbounded domains. II. Equations with time delays

*JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS*, *225*(2), 557–586.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

1998 review

Theory and applications of partial functional differential equations. By Jianhong Wu.

[Review of ]. *SIAM Review*, *40*(3), 746–747.

Source: NC State University Libraries

Added: August 6, 2018

1997 article

Dynamics of reaction-diffusion systems and applications

Pao, C. V. (1997, December). *NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS*, Vol. 30, pp. 3371–3377.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

1997 chapter

Dynamics of weakly coupled parabolic systems with nonlocal boundary conditions

In S. Sivasundaram & A. A. Martynyuk (Eds.), *Advances in nonlinear dynamics* (Vol. 5, pp. 319–327). Australia: Gordon and Breach.

Ed(s): . S. Sivasundaram & A. Martynyuk

Source: NC State University Libraries

Added: August 6, 2018

1997 journal article

Systems of parabolic equations with continuous and discrete delays

*JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS*, *205*(1), 157–185.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

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