Existence of Solutions for the Evolution 𝑝𝑥-Laplacian Equation Not in Divergence FormReport as inadecuate




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Journal of Applied MathematicsVolume 2012 2012, Article ID 835495, 21 pages

Research ArticleDepartment of Mathematics, Jilin University, Changchun 130012, China

Received 31 October 2011; Accepted 6 December 2011

Academic Editor: Hui-Shen Shen

Copyright © 2012 Changchun Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The existence of weak solutions is studied to the initial Dirichlet problemof the equation 𝑢𝑡=𝑢div|∇𝑢|𝑝𝑥−2∇𝑢, with inf 𝑝𝑥>2. We adopt the method of parabolic regularization. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence of weak solutions.





Author: Changchun Liu, Junchao Gao, and Songzhe Lian

Source: https://www.hindawi.com/



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