# American Institute of Mathematical Sciences

April  2021, 26(4): 1797-1809. doi: 10.3934/dcdsb.2021028

## 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

Received  July 2020 Revised  December 2020 Published  January 2021

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.

Citation: Chueh-Hsin Chang, Chiun-Chuan Chen, Chih-Chiang Huang. Traveling wave solutions of a free boundary problem with latent heat effect. Discrete & Continuous Dynamical Systems - B, 2021, 26 (4) : 1797-1809. doi: 10.3934/dcdsb.2021028
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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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