This article is cited in 1 paper

Mathematics

The heat equation in a medium with nonuniformly distributed nonlinear heat sources or absorbers

A. S. Kalashnikov


Abstract: For a heat conduction equation with non-linear sources whose action intensifies at infinity, it is proved that the Cauchy problem has no locally bounded solution in any time interval. In the case of non-linear heat absorption decaying at infinity, necessary and sufficient conditions are found for instantaneous compactification of the support of the solution for the Cauchy problem.

UDC: 517.356+517.958

Received: 10.11.1982

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