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Liouville theorems, a priori estimates, and blow-up rates for solutions of indefinite superlinear parabolic problems

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Abstract

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.

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Authors and Affiliations

  1. Nashville, USA

    Juraj Földes Nashville

  2. Vanderbilt University, Nasvhille, TN, 37240, USA

    Juraj Földes Nashville

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  1. Juraj Földes Nashville
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Nashville, J.F. Liouville theorems, a priori estimates, and blow-up rates for solutions of indefinite superlinear parabolic problems. Czech Math J 61, 169–198 (2011). https://doi.org/10.1007/s10587-011-0005-2

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