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Finite-time quenching of competing species with constrained boundary evaporation

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  • We consider a class of SKT type reaction-cross diffusion models with vanishing random diffusion coefficients. For homogeneous Dirichlet boundary conditions we prove non-existence of global-in-time non-trivial non-negative smooth solutions. Some numerical results are also presented, suggesting the possibility of finite-time extinction.
    Mathematics Subject Classification: Primary: 35K51, 35B60; Secondary: 92D25.

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