Xiao-Biao Lin

Works (23)

Updated: April 11th, 2023 10:13
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2019 journal article

Chaotic Traveling Wave Solutions in Coupled Chua's Circuits

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 31(3), 1373–1396.

By: F. Geng*, X. Lin & X. Liu *

author keywords: Coupled Chua's circuits; Traveling waves; Heteroclinic orbits; Shilnikov's chaos; Melnikov integral
Source: Web Of Science
Added: September 9, 2019

2017 journal article

Codiagonalization of matrices and existence of multiple homoclinic solutions

Journal of Applied Analysis and Computation, 7(1), 172–188.

By: X. Lin & C. Zhu

Source: NC State University Libraries
Added: August 6, 2018

2017 journal article

SADDLE-NODE BIFURCATIONS OF MULTIPLE HOMOCLINIC SOLUTIONS IN ODES

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 22(4), 1435–1460.

By: X. Lin & C. Zhu

author keywords: Degenerate homoclinic bifurcation; Lyapunov-Schmidt reduction; exponential dichotomy; codiagonalization of quadratic forms
Source: Web Of Science
Added: August 6, 2018

2016 journal article

Stability of Concatenated Traveling Waves

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 28(3-4), 867–896.

By: X. Lin & S. Schecter

author keywords: Interaction of waves; Reaction-diffusion equation; Spatial dynamics; Laplace transform; Exponential dichotomy in trace space
Source: Web Of Science
Added: August 6, 2018

2015 journal article

Multiple transverse homoclinic solutions near a degenerate homoclinic orbit

JOURNAL OF DIFFERENTIAL EQUATIONS, 259(1), 1–24.

By: X. Lin, B. Long* & C. Zhu *

author keywords: Degenerate homoclinic bifurcation; Lyapunov-Schmidt reduction; Exponential dichotomies; Chaotic motions; Codiagonalization of quadratic forms
Source: Web Of Science
Added: August 6, 2018

2015 article

Multiple transverse homoclinic solutions near a degenerate homoclinic orbit (vol 259, pg 1, 2015)

Lin, X.-B., Long, B., & Zhu, C. (2015, December 5). JOURNAL OF DIFFERENTIAL EQUATIONS, Vol. 259, pp. 6885–6886.

By: X. Lin, B. Long* & C. Zhu *

Source: Web Of Science
Added: August 6, 2018

2015 journal article

Stability of concatenated traveling waves: Alternate approaches

JOURNAL OF DIFFERENTIAL EQUATIONS, 259(7), 3144–3177.

By: X. Lin & S. Schecter

author keywords: Traveling wave; Stability; Spatial dynamics; Laplace transform; Exponential dichotomy
Source: Web Of Science
Added: August 6, 2018

2014 journal article

TRANSONIC EVAPORATION WAVES IN A SPHERICALLY SYMMETRIC NOZZLE

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 46(2), 1472–1504.

By: X. Lin & M. Wechselberger

author keywords: evaporation waves; blow-up technique; geometric singular perturbation theory
Source: Web Of Science
Added: August 6, 2018

2013 journal article

Stability of standing waves for monostable reaction-convection equations in a large bounded domain with boundary conditions

JOURNAL OF DIFFERENTIAL EQUATIONS, 255(1), 58–84.

By: X. Lin

author keywords: Traveling waves; KPP/Fisher equations; Stability on large intervals; Weighted norms; Exponential dichotomies; Lambda Lemma
Source: Web Of Science
Added: August 6, 2018

2013 journal article

Traveling wave solutions in coupled Chua's circuits, part I: Periodic solutions

Journal of Applied Analysis and Computation, 3(3), 213–237.

By: S. Chow, M. Jiang & X. Lin

Source: NC State University Libraries
Added: August 6, 2018

2012 journal article

STANDING WAVES FOR PHASE TRANSITIONS IN A SPHERICALLY SYMMETRIC NOZZLE

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 44(1), 405–436.

By: H. Fan & X. Lin

author keywords: liquid/vapor phase transition; spherically symmetric nozzle; internal layer solution; singular perturbation; numerical shooting method
Source: Web Of Science
Added: August 6, 2018

2011 journal article

Traveling Wave Solutions for a Predator-Prey System With Sigmoidal Response Function

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 23(4), 903–921.

By: X. Lin, P. Weng* & C. Wu*

author keywords: Traveling wave solution; Shooting method; Wazewski set; Egress set; LaSalle's invariance principle
Source: Web Of Science
Added: August 6, 2018

2010 journal article

Collapsing and Explosion Waves in Phase Transitions with Metastability, Existence, Stability and Related Riemann Problems

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 22(2), 163–191.

By: H. Fan* & X. Lin

author keywords: Liquid/vapor phase transition; Collapsing and explosion waves; Phase boundary; Reaction-diffusion-convection equation; Admissibility criterion for Riemann solutions
Source: Web Of Science
Added: August 6, 2018

2009 journal article

Algebraic dichotomies with an application to the stability of Riemann solutions of conservation laws

JOURNAL OF DIFFERENTIAL EQUATIONS, 247(11), 2924–2965.

By: X. Lin

author keywords: Algebraic dichotomy; Conservation laws; Dafermos regularization; Stability of Riemann solutions; Analytic semigroup; Singular perturbations
Source: Web Of Science
Added: August 6, 2018

2007 journal article

Gearhart-Pruss theorem and linear stability for riemann solutions of conservation laws

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 19(4), 1037–1074.

By: X. Lin

author keywords: Gearhart Pruss theorem; conservation laws; Riemann solutions; C-0-semigroup; resonance values
Source: Web Of Science
Added: August 6, 2018

2006 journal article

Fast solvers for 3D Poisson equations involving interfaces in a finite or the infinite domain

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 191(1), 106–125.

By: M. Lai*, Z. Li  & X. Lin

author keywords: arbitrary interface; fast 3D Poisson solver; immersed interface method; infinite domain; extension of jumps; spherical coordinates; level set function; artificial boundary condition
Sources: Web Of Science, ORCID
Added: August 6, 2018

2006 journal article

Slow eigenvalues of self-similar solutions of the Dafermos regularization of a system of conservation laws: An analytic approach

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 18(1), 1–52.

By: X. Lin

author keywords: conservation law; Riemann solution; Dafermos regularization; stability; eigenvalue; eigenfunction; SLEP method; asymptotic expansion
Source: Web Of Science
Added: August 6, 2018

2005 journal article

L-2 semigroup and linear stability for Riemann solutions of conservation laws

Dynamics of Partial Differential Equations, 2(4), 301–333.

By: X. Lin

Source: NC State University Libraries
Added: August 6, 2018

2003 journal article

Stability of self-similar solutions of the Dafermos regularization of a system of conservation laws

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 35(4), 884–921.

By: X. Lin & S. Schecter

author keywords: conservation law; Riemann problem; Dafermos regularization; stability; spectrum; singular perturbation
Source: Web Of Science
Added: August 6, 2018

2002 journal article

Heteroclinic and periodic cycles in a perturbed convection model

JOURNAL OF DIFFERENTIAL EQUATIONS, 182(1), 219–265.

By: X. Lin & I. Vivancos*

author keywords: singular perturbations; heteroclinic bifurcations; relay non-linearity; Melnikov's method; dynamo process; symmetry
Source: Web Of Science
Added: August 6, 2018

2001 journal article

Construction and asymptotic stability of structurally stable internal layer solutions

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 353(8), 2983–3043.

By: X. Lin

author keywords: singular perturbation; matched asymptotic expansion; internal layers; critical eigenvalues; stability; structural stability
Source: Web Of Science
Added: August 6, 2018

2000 journal article

Generalized Rankine-Hugoniot condition and shock solutions for quasilinear hyperbolic systems

JOURNAL OF DIFFERENTIAL EQUATIONS, 168(2), 321–354.

By: X. Lin

Source: Web Of Science
Added: August 6, 2018

1999 journal article

Multiple internal layer solutions generated by spatially oscillatory perturbations

JOURNAL OF DIFFERENTIAL EQUATIONS, 154(2), 364–418.

By: J. Hale* & X. Lin

Source: Web Of Science
Added: August 6, 2018