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

  • * Corresponding author: Chueh-Hsin Chang

    * Corresponding author: Chueh-Hsin Chang 
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  • 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.

    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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