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Spatial behavior for nonlinear heat equations
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DOI：10.1142/S0218202597000335.png)
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Abstract
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In this paper we investigate spatial decay and growth estimates for the solutions of the nonlinear heat equation in a three-dimensional cylinder with homogeneous Dirichlet conditions prescribed on the lateral surface for all time. We derive two Phragmen-Lindelof type growth-decay estimates. Two methods are used in our approximation. One of them involves a measure on the cross-sections and the other uses the ''energy'' contained in the part of the cylinder beyond a cross-section. For suitable volumetric heat capacity and thermal conductivity the second-order approximation combined with comparison arguments allow us to improve the decay estimates. We also sketch the application of the first-order method in the case where the solid is a cone. Spatial estimates for the backward nonlinear equation are presented in the last section.
Keywords:
PARABOLIC PROBLEMS
DECAY
CONDUCTION
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