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Blow-up phenomena for a class of quasilinear parabolic problems under Robin boundary condition. (English) Zbl 1206.35151
Summary: This note deals with a class of heat emission processes in a medium with a non-negative source, a nonlinear decreasing thermal conductivity and a linear radiation (Robin) boundary condition. For such heat emission problems, we make use of a first-order differential inequality technique to establish conditions on the data sufficient to guarantee that the blow-up of the solutions does occur or does not occur. In addition, the same technique is used to determine a lower bound for the blow-up time when blow-up occurs.

35K59Quasilinear parabolic equations
35K20Second order parabolic equations, initial boundary value problems
35B44Blow-up (PDE)
Full Text: DOI
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