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Liouville theorems, a priori estimates, and blow-up rates for solutions of indefinite superlinear parabolic problems. (English) Zbl 1224.35013

Summary: In this paper we establish new nonlinear Liouville theorems for parabolic problems on half spaces. Based on the Liouville theorems, we derive estimates for the blow-up of positive solutions of indefinite parabolic problems and investigate the complete blow-up of these solutions. We also discuss a priori estimates for indefinite elliptic problems.

MSC:

35B09 Positive solutions to PDEs
35B44 Blow-up in context of PDEs
35B45 A priori estimates in context of PDEs
35B53 Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs
35J61 Semilinear elliptic equations
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