Title

A variational formulation of the Nagumo reaction-diffusion equation and the Nagumo telegraph equation

Authors

Authors

R. A. Van Gorder;K. Vajravelu

Comments

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Abbreviated Journal Title

Nonlinear Anal.-Real World Appl.

Keywords

Nagumo reaction-diffusion equation; Nagumo telegraph equation; Numerical; solution; Mathematics, Applied

Abstract

We consider the Nagumo reaction-diffusion equation u(t) = u(xx) + f(u) and the Nagumo telegraph equation tau u(tt) + (1 - tau f'(u))u(t) = u(xx) + f(u), where f(u) = u(a - u)(1 - u) as boundary value problems over the finite spatial interval x is an element of [0, L] and finite time t is an element of [0, t*]. We are able to obtain approximate solutions for the boundary value problems via a variational technique. Also, we obtain numerical solutions for some special cases, in order to demonstrate the validity of the variational technique. Also, these numerical solutions are used to discuss the qualitative characteristics of the solutions for the specific initial data considered. (C) 2009 Elsevier Ltd. All rights reserved.

Journal Title

Nonlinear Analysis-Real World Applications

Volume

11

Issue/Number

4

Publication Date

1-1-2010

Document Type

Article

Language

English

First Page

2957

Last Page

2962

WOS Identifier

WOS:000279524300070

ISSN

1468-1218

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