Travelling Wavefronts in Reaction-Diffusion Equations with Convection Effects and Non-Regular Terms
✍ Scribed by Luisa Malaguti; Cristina Marcelli
- Publisher
- John Wiley and Sons
- Year
- 2002
- Tongue
- English
- Weight
- 233 KB
- Volume
- 242
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
This paper deals with the appearance of monotone bounded travelling wave solutions for a parabolic reaction-diffusion equation which frequently meets both in chemical and biological systems. In particular, we prove the existence of monotone front type solutions for any wave speed c ≥ c * and give an estimate for the threshold value c * .
Our model takes into account both of a density dependent diffusion term and of a non-linear convection effect. Moreover, we do not require the main non-linearity g to be a regular C 1 function; in particular we are able to treat both the case when g (0) = 0, giving rise to a degenerate equilibrium point in the phase plane, and the singular case when g (0) = +∞. Our results generalize previous ones due to