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2011, 2011(Special): 22-31. doi: 10.3934/proc.2011.2011.22

Well-posedness and large-time behaviors of solutions for a parabolic equation involving $p(x)$-Laplacian

Goro Akagi 1, and  Kei Matsuura 2,

1. 

Department of Machinery and Control Systems, College of Systems Engineering and Science,, Shibaura Institute of Technology, 307 Fukasaku, Minuma-ku, Saitama-shi, Saitama 337-8570
2. 

Research Institute for Science Engineering, Waseda University, Okubo 3-4-1, Shinjuku-ku, Tokyo 169-8555, Japan

Received  July 2010 Revised  August 2011 Published  September 2011

This paper is concerned with the initial-boundary value problem for a nonlinear parabolic equation involving the so-called $p(x)$-Laplacian. A subdifferential approach is employed to obtain a well-posedness result as well as to investigate large-time behaviors of solutions.
Keywords: $p(x)$-Laplacian, subdifferential, parabolic equation, variable exponent Lebesgue and Sobolev spaces.
Mathematics Subject Classification: Primary: 35K55, 46E30; Secondary: 35K90.
Citation: Goro Akagi, Kei Matsuura. Well-posedness and large-time behaviors of solutions for a parabolic equation involving $p(x)$-Laplacian. Conference Publications, 2011, 2011 (Special) : 22-31. doi: 10.3934/proc.2011.2011.22
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