# Asymptotic behavior of the numerical solutions of time-delayed reaction diffusion equations with non-monotone reaction term

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 37, Issue: 2, page 259-276
- ISSN: 0764-583X

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topWang, Yuan-Ming. "Asymptotic behavior of the numerical solutions of time-delayed reaction diffusion equations with non-monotone reaction term." ESAIM: Mathematical Modelling and Numerical Analysis 37.2 (2010): 259-276. <http://eudml.org/doc/194162>.

@article{Wang2010,

abstract = {
This paper is concerned with the asymptotic behavior of the
finite difference solutions of a class of nonlinear reaction diffusion equations with time delay.
By introducing a pair of coupled upper and lower solutions, an
existence result of the solution is given and
an attractor of the solution is obtained without monotonicity assumptions on the nonlinear reaction function.
This attractor is a sector between two coupled quasi-solutions of the corresponding “steady-state" problem, which are obtained from
a monotone iteration process. A sufficient condition, ensuring that two coupled quasi-solutions
coincide, is given. Also given is the application to a nonlinear reaction diffusion problem with time delay for three different types of reaction functions, including some numerical results which validate the theoretical analysis.
},

author = {Wang, Yuan-Ming},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Asymptotic behavior; finite difference equation;
reaction diffusion equation; time delay; upper and lower solutions.; upper and lower solutions},

language = {eng},

month = {3},

number = {2},

pages = {259-276},

publisher = {EDP Sciences},

title = {Asymptotic behavior of the numerical solutions of time-delayed reaction diffusion equations with non-monotone reaction term},

url = {http://eudml.org/doc/194162},

volume = {37},

year = {2010},

}

TY - JOUR

AU - Wang, Yuan-Ming

TI - Asymptotic behavior of the numerical solutions of time-delayed reaction diffusion equations with non-monotone reaction term

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 37

IS - 2

SP - 259

EP - 276

AB -
This paper is concerned with the asymptotic behavior of the
finite difference solutions of a class of nonlinear reaction diffusion equations with time delay.
By introducing a pair of coupled upper and lower solutions, an
existence result of the solution is given and
an attractor of the solution is obtained without monotonicity assumptions on the nonlinear reaction function.
This attractor is a sector between two coupled quasi-solutions of the corresponding “steady-state" problem, which are obtained from
a monotone iteration process. A sufficient condition, ensuring that two coupled quasi-solutions
coincide, is given. Also given is the application to a nonlinear reaction diffusion problem with time delay for three different types of reaction functions, including some numerical results which validate the theoretical analysis.

LA - eng

KW - Asymptotic behavior; finite difference equation;
reaction diffusion equation; time delay; upper and lower solutions.; upper and lower solutions

UR - http://eudml.org/doc/194162

ER -

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