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Energy solutions of the Cauchy-Neumann problem for porous medium equations

Pages: 1 - 10, Issue Special, September 2009

 Abstract        Full Text (172.9K)              

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)

Abstract: The existence of energy solutions to the Cauchy-Neumann problem for the porous medium equation of the form $v_t - \Delta (|v|^{m-2}v) = \alpha v$ with $m \geq 2$ and $\alpha \in \mathbb{R}$ is proved, by reducing the equation to an evolution equation involving two subdifferential operators and exploiting subdifferential calculus recently developed by the author.

Keywords:  Porous medium equation, Neumann boundary condition, subdifferential operator, doubly nonlinear evolution equation, reflexive Banach space
Mathematics Subject Classification:  35K65, 35K55; Secondary: 47J35

Received: August 2008;      Revised: February 2009;      Published: September 2009.