Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 1057–1068
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
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.
partial differential equations, nonlinear parabolic heat equation, existence and uniqueness theorem, exact solution.
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Received May 28, 2019, published August 7, 2019
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
Citation in format AMSBIB
\paper On exact solutions to a heat wave propagation boundary-value problem for a nonlinear heat equation
\jour Sib. \`Elektron. Mat. Izv.
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