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Heat propagation in linear and nonlinear media with strongly nonstationary properties

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Abstract

We consider a first boundary-value problem in a quadrant of the plane for a second-order linear parabolic equation with two independent variables. The boundary function may increase along with the time variable. We show that the solution remains bounded at interior points when the highest-order coefficient decreases sufficiently rapidly or when the lowest order coefficients, having appropriate signs, increase sufficiently rapidly. Similar results are established for certain quasilinear nonuniformly parabolic equations. Examples are constructed showing the accuracy of the results obtained.

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Authors
  1. A. S. Kalashnikov
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Additional information

Translated from Trudy Seminara im. I. G. Petrovskogo, No. 12, pp. 137–148, 1987.

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Kalashnikov, A.S. Heat propagation in linear and nonlinear media with strongly nonstationary properties. J Math Sci 47, 2585–2595 (1989). https://doi.org/10.1007/BF01105912

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  • DOI: https://doi.org/10.1007/BF01105912

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