Xiao-Biao Lin

Works (23)

Updated: April 4th, 2024 17:40

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 n & X. Liu*

author keywords: Coupled Chua's circuits; Traveling waves; Heteroclinic orbits; Shilnikov's chaos; Melnikov integral
UN Sustainable Development Goal Categories
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 n & S. Schecter n

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 n, 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 n, 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 n & S. Schecter n

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
TL;DR: The existence and uniqueness of evaporation waves that cross from supersonic to subsonic regions and evapation waves that connect from the subsono-subsonic region to the sonic surface and then continue onto the su personic b... (via Semantic Scholar)
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
TL;DR: The proof of the existence of an exact standing wave solution near the singular limit is based on the geometric singular perturbation theory and is outlined in the paper. (via Semantic Scholar)
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 n, 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 n

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 n

author keywords: Algebraic dichotomy; Conservation laws; Dafermos regularization; Stability of Riemann solutions; Analytic semigroup; Singular perturbations
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
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 n

author keywords: Gearhart Pruss theorem; conservation laws; Riemann solutions; C-0-semigroup; resonance values
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
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, NC State University Libraries
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 n

author keywords: conservation law; Riemann solution; Dafermos regularization; stability; eigenvalue; eigenfunction; SLEP method; asymptotic expansion
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
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 n

UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
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
TL;DR: It is shown, by studying the essential spectrum of the linearized system in a weighted function space, that stability is determ ined by eigenvalues only. (via Semantic Scholar)
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
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 n

author keywords: singular perturbation; matched asymptotic expansion; internal layers; critical eigenvalues; stability; structural stability
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities (OpenAlex)
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*

UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
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 n

UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

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