A review on travelling wave solutions of one-dimensional reaction diffusion equations with non-linear diffusion term
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 no...
| Main Authors: | , , |
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| Format: | Journal article |
| Published: |
1996
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| Summary: | 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 diffusive-aggregative process. In this case the travelling wave solutions are explored and the ill-posedness of two boundary-value problems associated with the above equation is stated. |
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