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On the Form of Smooth-Front Travelling Waves in a Reaction-Diffusion Equation with Degenerate Nonlinear Diffusion

J.A. Sherratt (2010)

Mathematical Modelling of Natural Phenomena

Reaction-diffusion equations with degenerate nonlinear diffusion are in widespread use as models of biological phenomena. This paper begins with a survey of applications to ecology, cell biology and bacterial colony patterns. The author then reviews mathematical results on the existence of travelling wave front solutions of these equations, and their generation from given initial data. A detailed study is then presented of the form of smooth-front...

On the radius of spatial analyticity for the higher order nonlinear dispersive equation

Aissa Boukarou, Kaddour Guerbati, Khaled Zennir (2022)

Mathematica Bohemica

In this work, using bilinear estimates in Bourgain type spaces, we prove the local existence of a solution to a higher order nonlinear dispersive equation on the line for analytic initial data u 0 . The analytic initial data can be extended as holomorphic functions in a strip around the x -axis. By Gevrey approximate conservation law, we prove the existence of the global solutions, which improve earlier results of Z. Zhang, Z. Liu, M. Sun, S. Li, (2019).

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