Abstract
We find an explicit form of entropy solution to a Riemann problem for a degenerate nonlinear parabolic equation with piecewise constant velocity and diffusion coefficients. It is demonstrated that this solution corresponds to the minimum point of some strictly convex function of a finite number of variables. We also discuss the limit when piecewise constant coefficients approximate the arbitrary ones.
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The research was partially supported by the Russian Science Foundation, Grant 22-21-00344.
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Panov, E.Y. On the Structure of Entropy Solutions to the Riemann Problem for a Degenerate Nonlinear Parabolic Equation. J Dyn Diff Equat (2024). https://doi.org/10.1007/s10884-024-10361-y
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DOI: https://doi.org/10.1007/s10884-024-10361-y