Traveling wave solutions of a free boundary problem with latent heat effect

Chueh-Hsin Chang; Chiun-Chuan Chen; Chih-Chiang Huang

doi:10.3934/dcdsb.2021028

Article Contents

2021, Volume 26, Issue 4: 1797-1809. Doi: 10.3934/dcdsb.2021028

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Traveling wave solutions of a free boundary problem with latent heat effect

1.
Department of Applied Mathematics, Tunghai University, Tunghai University, Taichung, 40704, Taiwan
2.
Department of Mathematics, National Taiwan University, National Taiwan University, Taipei, 10617, Taiwan

^* Corresponding author: Chueh-Hsin Chang
^* Corresponding author: Chueh-Hsin Chang

Received: June 30, 2020

Revised: November 30, 2020

Early access: January 2021

Published: April 2021

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Abstract

We study a free boundary problem of two competing species with latent heat effect. We establish the existence and uniqueness of the traveling wave solution and derive upper and lower bounds for the wave speed. Especially our results show that the latent heat retards propagation of the waves.

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Mathematics Subject Classification: 35K57, 35C07, 35R35.

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Figure 1. The intersection between $ y = \lambda c $ and $ y = g(c) $, and the zeros of $ g(c) = 0 $ under three cases: Figure (a): $ g(0)>0 $, $ 0<c_{ \lambda }<c_{0}<c_{min,u} $. Figure (b): $ g(0) = 0 $, $ c_{\lambda } = c_{0} = 0 $, Figure (c): $ g(0)<0 $, $ c_{min,v}<c_{0}<c_{\lambda }<0 $

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