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Zbl 1180.35317
Mu, Chunlai; Zhou, Shouming; Liu, Dengming
Quenching for a reaction-diffusion system with logarithmic singularity. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 11, A, 5599-5605 (2009). ISSN 0362-546X

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 2000:: *35K67
35B25 Singular perturbations (PDE)
35B33 Critical exponents
35K58
35K51
35K57 Reaction-diffusion equations

Keywords: non-simultaneous quenching; quenching rate; positive Dirichlet boundary conditions

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Zentralblatt MATH Berlin [Germany]