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Quenching for a reaction-diffusion system with logarithmic singularity. (English) Zbl 1180.35317
Summary: We study the quenching phenomenon for a reaction-diffusion system with singular logarithmic source terms and positive Dirichlet boundary conditions. Some sufficient conditions for quenching of the solutions in finite time are obtained, and the blow-up of time-derivatives at the quenching point is verified. Furthermore, under appropriate hypotheses, the non-simultaneous quenching of the system is proved, and the estimates of quenching rate is given.
MSC:
35K67Singular parabolic equations
35B25Singular perturbations (PDE)
35B33Critical exponents (PDE)
35K58Semilinear parabolic equations
35K51Second-order parabolic systems, initial bondary value problems
35K57Reaction-diffusion equations