A degenerate parabolic system with localized sources and nonlocal boundary condition

Abstract

This paper deals with the blow-up properties of the positive solutions to a degenerate parabolic system with localized sources and nonlocal boundary conditions. We investigate the influence of the reaction terms, the weight functions, local terms and localized source on the blow-up properties. We will show that the weight functions play the substantial roles in determining whether the solutions will blow-up or not, and obtain the blow-up conditions and its blow-up rate estimate.

Keywords

Nonlocal boundary condition / localized sources / blow-up rate / Porous medium equation

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