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.2012.49.6.1179
Published 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  


Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd