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

Pages: 22 - 31, Issue Special, September 2011

 Abstract        Full Text (127.9K)              

Goro Akagi - 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, Japan (email)
Kei Matsuura - Research Institute for Science Engineering, Waseda University, Okubo 3-4-1, Shinjuku-ku, Tokyo 169-8555, Japan (email)

Abstract: 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

Received: July 2010;      Revised: August 2011;      Published: September 2011.