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A review on travelling wave solutions of one-dimensional reaction diffusion equations with non-linear diffusion term

Abstract:

In this paper we review the existence of different types of travelling wave solutions $u(x,t) = \phi(x - ct)$ of degenerate non-linear reaction-diffusion equations of the form $u_t = [D(u)u_x]_x + g(u)$ for different density-dependent diffusion coefficients D and kinetic part g. These include the non-linear degenerate generalized Fisher-KPP and the Nagumo equations. Also, we consider an equation whose diffusion coefficient changes sign as the diffusive substance increases. This describes a di...

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F. Sánchez-Garduño More by this author
P. K. Maini More by this author
Publication date:
1996
URN:
uuid:1e4f980f-fcbd-4bb0-b43b-5b6c3fc56e5e
Local pid:
oai:eprints.maths.ox.ac.uk:569

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