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

Shin-Yi Lee; Shin-Hwa Wang; Chiou-Ping Ye

doi:10.3934/proc.2005.2005.587

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2005, Volume 2005: 587-596. Doi: 10.3934/proc.2005.2005.587 open access

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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

1.
Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 300, Republic of China
2.
Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 300

Received: June 30, 2004

Revised: March 31, 2005

Published: August 2005

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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.

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Mathematics Subject Classification: 35J65, 34B15.

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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

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