Non-sharp travelling waves for a dual porous medium equation

Jing  Li; Yifu Wang; Jingxue Yin

doi:10.3934/cpaa.2016.15.623

Article Contents

2016, Volume 15, Issue 2: 623-636. Doi: 10.3934/cpaa.2016.15.623

This issue Previous Article Existence and concentration of semiclassical solutions for Hamiltonian elliptic system Next Article Asymptotic analysis of a spatially and size-structured population model with delayed birth process

Non-sharp travelling waves for a dual porous medium equation

1.
College of Science, Minzu University of China, Beijing, 100081
2.
Department of Mathematics, Beijing Institute of Technology, Beijing 100081
3.
Department of Mathematics, South China Normal University, Guangzhou, Guangdong, 510631

Received: January 31, 2015

Revised: September 30, 2015

Published: February 2016

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Abstract

We discuss non-sharp travelling waves of a dual porous medium equation with monostable source and bistable source respectively. We show the existence of non-sharp travelling waves and find that though the equation is degenerate, the travelling waves are classical ones. Furthermore, for the monostable source, we show that the non-sharp travelling waves are infinite, while for the bistable source, the non-sharp travelling waves are semi-finite, which is in contrast with the case of the heat equation.

Keywords:

Travelling wave,
dual porous medium equation.

Mathematics Subject Classification: Primary: 35K65, 35K40.

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