On the viscosity solutions to a class of nonlinear degenerate parabolic differential equations

Tilak Bhattacharya; Leonardo Marazzi

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arXiv · 1610.03549

On the viscosity solutions to a class of nonlinear degenerate parabolic differential equations

Tilak Bhattacharya·Leonardo Marazzi

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Abstract

In this work, we show existence and uniqueness of positive solutions of $H(Du, D^2u)+\chi(t)|Du|^\Gamma-f(u)u_t=$ in $\Omega\times(0, T)$ and $u=h$ on its parabolic boundary. The operator $H$ satisfies certain homogeneity conditions, $\Gamma>0$ and depends on the degree of homogeneity of $H$, $f>0$, increasing and meets a concavity condition. We also consider the case $f\equiv 1$ and prove existence of solutions without sign restrictions.

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Tilak Bhattacharya, Leonardo Marazzi. 2016-10-11. On the viscosity solutions to a class of nonlinear degenerate parabolic differential equations. https://arxiv.org/abs/1610.03549

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