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

    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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