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

Abstract

In this work, we show existence and uniqueness of positive solutions of $H(Du,D^{2}u)+\chi (t)|Du{|}^{\Gamma }-f(u)u_t=$ 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.

31 pages. This version has fewer typos