Nonsharp travelling wave fronts in the Fisher equation with degenerate nonlinear diffusion

Travelling Wave Solution of the Fisher-Kolmogorov Equation with Non-Linear Diffusion

In this paper we study one-dimensional Fisher-Kolmogorov equation with density dependent non-linear diffusion. We choose the diffusion as a function of cell density such that it is high in highly cell populated areas and it is small in the regions of fewer cells. The Fisher equation with non-linear diffusion is known as modified Fisher equation. We study the travelling wave solution of modified...

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

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 detail...

Travelling Wave Solutions and Conservation Laws of Fisher-Kolmogorov Equation

Lie symmetry group method is applied to study the Fisher-Kolmogorov equation. The symmetry group is given, and travelling wave solutions are obtained. Finally the conservation laws are determined.

Existence and Asymptotic Behavior of Traveling Wave Fronts for a Time-Delayed Degenerate Diffusion Equation

and Applied Analysis 3 (a) (b) Figure 1: Sharp-type traveling wave fronts. (a) Monotonic increasing. (b) Monotonic decreasing. (a) (b) Figure 2: Smooth-type traveling wave fronts. (a) Monotonic increasing. (b) Monotonic decreasing. Clearly, for any given φ > 0, if

Travelling Wave Solutions of the One Dimensional Diffusion-reaction Equation