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Global existence and blow-up of solutions for p-Laplacian evolution equation with nonlinear memory term and nonlocal boundary condition

Zhong Bo Fang* and Jianyun Zhang

Author Affiliations

School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, P.R. China

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Boundary Value Problems 2014, 2014:8  doi:10.1186/1687-2770-2014-8

Published: 7 January 2014


In this paper, we deal with an initial boundary value problem for a p-Laplacian evolution equation with nonlinear memory term and inner absorption term subject to a weighted linear nonlocal boundary condition. We find the effects of a weighted function as regards determining blow-up of nonnegative solutions or not and establish the precise blow-up estimate for the linear diffusion case under some suitable conditions.

p-Laplacian evolution equation; nonlinear memory; global existence; blow-up; weight function