## Vanishing latent heat limit in a Stefan-like problem arising in biology.(English)Zbl 1049.92035

Summary: We consider a two phase Stefan problem with a reaction term in arbitrary space dimension and prove that as the latent heat coefficient tends to zero, its weak solution converges to the weak solution of the corresponding problem with zero latent heat, which is obtained as the spatial segregation limit of a competition-diffusion system. In particular, we obtain a uniform convergence result for the corresponding interfaces in the one-dimensional case.

### MSC:

 92D40 Ecology 35K57 Reaction-diffusion equations 35R35 Free boundary problems for PDEs 35K65 Degenerate parabolic equations
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### References:

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