Bulletin of the
Korean Mathematical Society BKMS

In this paper, we consider a doubly nonlinear parabolic partial differential equation ${\partial{\beta(u)} \over \partial t}-\Delta_{p}u+f(x,t,u)=0$ in $\Omega \times [0,T],$ with Dirichlet boundary condition and initial data given. We prove the existence of a discrete approximate solution by means of the Rothe discretization in time method under some conditions on $\beta$, $f$ and $p$.

Keywords: doubly nonlinear, $p$-Laplacian, Rothe method

MSC numbers: 35K55, 35K45