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October 2014 Local solvability of a fully nonlinear parabolic equation
Goro Akagi
Kodai Math. J. 37(3): 702-727 (October 2014). DOI: 10.2996/kmj/1414674617

Abstract

This paper is concerned with the existence of local (in time) positive solutions to the Cauchy-Neumann problem in a smooth bounded domain of RN for some fully nonlinear parabolic equation involving the positive part function r $\in$ R $\mapsto$ (r)+: = r ∨ 0. To show the local solvability, the equation is reformulated as a mixed form of two different sorts of doubly nonlinear evolution equations in order to apply an energy method. Some approximated problems are also introduced and the global (in time) solvability is proved for them with an aid of convex analysis, an energy method and some properties peculiar to the nonlinearity of the equation. Moreover, two types of comparison principles are also established, and based on these, the local existence and the finite time blow-up of positive solutions to the original equation are concluded as the main results of this paper.

Citation

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Goro Akagi. "Local solvability of a fully nonlinear parabolic equation." Kodai Math. J. 37 (3) 702 - 727, October 2014. https://doi.org/10.2996/kmj/1414674617

Information

Published: October 2014
First available in Project Euclid: 30 October 2014

zbMATH: 1305.62243
MathSciNet: MR3273892
Digital Object Identifier: 10.2996/kmj/1414674617

Rights: Copyright © 2014 Tokyo Institute of Technology, Department of Mathematics

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Vol.37 • No. 3 • October 2014
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