Geodesic
Liouville theorems, a priori estimates, and blow-up rates for solutions of indefinite superlinear parabolic problems
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 1, pp. 169-198

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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.
DOI : 10.1007/s10587-011-0005-2
Classification : 35B09, 35B44, 35B45, 35B53, 35J61, 35K59
Keywords: a priori estimates; Liouville theorems; blow-up rate; positive solution; indefinite parabolic problem 
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Földes, Juraj. Liouville theorems, a priori estimates, and blow-up rates for solutions of indefinite superlinear parabolic problems. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 1, pp. 169-198. doi: 10.1007/s10587-011-0005-2

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