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Dynamics of measured valued solutions to a backward-forward heat equation. (English) Zbl 0747.35013

This paper deals with the asymptotic behavior of measure valued solutions to the initial value problem for a nonlinear heat conduction equation, in a bounded domain with Dirichlet or Neumann boundary conditions. The function \(q\) of the gradient is not assumed to be linear or monoton. The restrictions on \(q\) is the satisfaction of the Fourier inequality. Applications are given to problems where \(q\) is not monotone.

MSC:

35K55 Nonlinear parabolic equations
35K05 Heat equation
35B40 Asymptotic behavior of solutions to PDEs
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