Travelling waves for generalized Fisher-Kolmogorov equation with
discontinuous density dependent diffusion
- Michaela ZAHRADNÍKOVÁ,
- Pavel Drabek
Abstract
We are concerned with the existence and qualitative properties of
travelling wave solutions for a quasilinear reaction-diffusion equation
on the real line. We consider a non-Lipschitz reaction term of
Fisher--KPP type and a discontinuous diffusion coefficient that allows
for degenerations and singularities at equilibrium points. We
investigate the joint influence of the reaction and diffusion terms on
the existence and nonexistence of travelling waves and, assuming these
terms are of power-type near equilibria, we provide classification of
solutions based on their asymptotic properties. Our approach provides a
broad theoretical background for the mathematical treatment of rather
general models not only in population dynamics but also in other applied
sciences and engineering.06 May 2022Submitted to Mathematical Methods in the Applied Sciences 09 May 2022Submission Checks Completed
09 May 2022Assigned to Editor
14 May 2022Reviewer(s) Assigned
12 Aug 2022Review(s) Completed, Editorial Evaluation Pending
17 Aug 2022Editorial Decision: Accept