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Non-Newtonian polytropic filtration systems with nonlinear boundary conditions

Wanjuan Du* and Zhongping Li

Author Affiliations

College of Mathematic and Information, China West Normal University, Nanchong 637002, PR China

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Boundary Value Problems 2011, 2011:2  doi:10.1186/1687-2770-2011-2

Published: 21 June 2011


This article deals with the global existence and the blow-up of non-Newtonian polytropic filtration systems with nonlinear boundary conditions. Necessary and sufficient conditions on the global existence of all positive (weak) solutions are obtained by constructing various upper and lower solutions.

Mathematics Subject Classification (2000)

35K50, 35K55, 35K65

Polytropic filtration systems; Nonlinear boundary conditions; Global existence; Blow-up