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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.
##### MSC:
 35K58 Semilinear parabolic equations 35K20 Second order parabolic equations, initial boundary value problems 35B35 Stability of solutions of PDE
quenching time
##### References:
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