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 Doubly nonlinear parabolic equations involving $p$-Laplacian operators via time-discretization method Bull. Korean Math. Soc. 2012 Vol. 49, No. 6, 1179-1192 https://doi.org/10.4134/BKMS.2012.49.6.1179Published online November 30, 2012 Kiyeon Shin and Sujin Kang Pusan National University, Pusan National University Abstract : 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 Downloads: Full-text PDF