The classical porous media equation is
$$u_t - \Delta(u^m) = 0 \quad m>1.$$
Has the (degenerate) wave equation $$u_{tt} - \Delta(u^m) = 0$$ been subject of studies? What would the physical interpretation of such a wave equation be?
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$\begingroup$ How to interpret the equation for negative $u$? Or should $m$ be a odd integer? $\endgroup$– LeechLatticeCommented Apr 23, 2019 at 3:18
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1$\begingroup$ for $m=2$ and a minus sign in front of the Laplacian this is the zero-water-depth limit of the Boussinesq shallow-water wave equation $\endgroup$– Carlo BeenakkerCommented Apr 23, 2019 at 10:44
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$\begingroup$ @CarloBeenakker Thank you. Do you have a reference where such zero-water-depth limit is studied? $\endgroup$– RikuCommented Apr 23, 2019 at 10:53
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