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This article is cited in 21 scientific papers (total in 21 papers)
Differentical equations, dynamical systems and optimal control
On exact solutions to a heat wave propagation boundary-value problem for a nonlinear heat equation
A. L. Kazakov Matrosov Institute for System Dynamics and Control Theory SB RAS, 134, Lermontova str., Irkutsk, 664033, Russia
Abstract:
The paper deals with a nonlinear second order parabolic PDE, which is usually called “the nonlinear heat equation”. We construct and study a particular class of solutions having the form of a heat wave that propagates on a cold (zero) background with finite velocity. The equation degenerates on the front of a heat wave and its order decreases. This fact complicates the study. We prove a new existence and uniqueness theorem for a boundary-value problem with a given heat-wave front in the class of analytical functions. Also, we are looking for exact heat-wave type solutions. The construction of these solutions is reduced to integration of the nonlinear second order ODE with singularity.
Keywords:
partial differential equations, nonlinear parabolic heat equation, existence and uniqueness theorem, exact solution.
Received May 28, 2019, published August 7, 2019
Citation:
A. L. Kazakov, “On exact solutions to a heat wave propagation boundary-value problem for a nonlinear heat equation”, Sib. Èlektron. Mat. Izv., 16 (2019), 1057–1068
Linking options:
https://www.mathnet.ru/eng/semr1114 https://www.mathnet.ru/eng/semr/v16/p1057
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Abstract page: | 429 | Full-text PDF : | 205 | References: | 31 |
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