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A quenching criterion for a multi-dimensional parabolic problem due to a concentrated nonlinear source. (English) Zbl 1225.35121
Summary: A multi-dimensional parabolic first initial-boundary value problem with a concentrated nonlinear source is studied. A criterion for its solution to quench, in a finite time $t_q$, everywhere on the concentrated nonlinear source only is given. An upper bound for $t_q$ is also deduced. For illustration, an example is given.

35K58Semilinear parabolic equations
35K20Second order parabolic equations, initial boundary value problems
35B35Stability of solutions of PDE
Full Text: DOI
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