Analytic approximations of travelling wave solutions

Abstract

A method based on differential inequalities and the maximum principle is developed to construct analytic approdimations of travelling wave solutions of certain reaction–diffusion equations arising in biology. The approximations are asymptotic in the sense that they converge to the unique travelling wave on the real line as the wave speed goes to infinity. The cases of density-independent and density-dependent diffusion coefficients are considered.

Keywords:

• travelling waves
• small parameter
• analytic approximation
• comparison functions

AMS:

• 35K57
• 34K10

Additional information

Notes on contributors

Walter Kelley