Travelling wave solutions for doubly degenerate reaction-diffusion equations

Mahmoud Bakheet Ali Mansour

Abstract


This paper concerns a nonlinear doubly degenerate reaction–diffusion equation which appears in a bacterial growth model and is also of considerable mathematical interest. A travelling wave analysis for the equation is carried out. In particular, the qualitative behaviour of both sharp and smooth travelling wave solutions is analysed. This travelling wave behaviour is also verified by some numerical computations for a special case.

doi:10.1017/S144618111100054X

Keywords


density-dependent diffusion; nonlinear degenerate parabolic equations; travelling waves



DOI: http://dx.doi.org/10.21914/anziamj.v52i0.3298



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.