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Explicit necessary and sufficient conditions for the existence of a dead core solution of a p-laplacian steady-state reaction-diffusion problem

Pages: 587 - 596, Issue Special, August 2005

 Abstract        Full Text (187.4K)              

Shin-Yi Lee - Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 300, Republic of China, China (email)
Shin-Hwa Wang - Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 300, China (email)
Chiou-Ping Ye - Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 300, China (email)

Abstract: We establish explicit necessary and sufficient conditions for the existence of a dead core solution of a $p$-Laplacian steady-state reaction-diffusion problem. The gap is extremely small between the explicit necessary condition and the explicit sufficient condition for the existence of a dead core solution.

Keywords:  Reaction-diffusion problem, p-Laplacian, dead core solution, existence, uniqueness, Lipschitz condition.
Mathematics Subject Classification:  35J65, 34B15.

Received: July 2004;      Revised: April 2005;      Published: September 2005.