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Complete and energy blow-up in indefinite superlinear parabolic problems. (English) Zbl 1114.35093

Blow-up of solutions of a semilinear parabolic equation is studied. In the equation, the usual power nonlinearity is multiplied by a coefficient which depends on the spatial variable and changes sign. It is shown that the solutions never blow-up completely in the whole domain. Sufficient conditions for blow-up of the associated energy functional are also given.

MSC:

35K55 Nonlinear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
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