# DOUBLY NONLINEAR PARABOLIC EQUATIONS INVOLVING p-LAPLACIAN OPERATORS VIA TIME-DISCRETIZATION METHOD

• Shin, Kiyeon (Department of Mathematics Pusan National University) ;
• Kang, Sujin (Department of Nanomaterials Engineering Pusan National University)
• Published : 2012.11.30

#### Abstract

In this paper, we consider a doubly nonlinear parabolic partial differential equation $\frac{{\partial}{\beta}(u)}{{\partial}t}-{\Delta}_pu+f(x,t,u)=0$ 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 $p$.

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