Blow up threshold for a parabolic type equation involving space integral and variational structure

Baiyu  Liu; Li  Ma

doi:10.3934/cpaa.2015.14.2169

Article Contents

2015, Volume 14, Issue 6: 2169-2183. Doi: 10.3934/cpaa.2015.14.2169

This issue Previous Article Homogenization of bending theory for plates; the case of oscillations in the direction of thickness Next Article On some semilinear equation in $R^4$ containing a Laplacian term and involving nonlinearity with exponential growth

Blow up threshold for a parabolic type equation involving space integral and variational structure

Baiyu Liu^1, and
Li Ma^2,

1.
School of Mathematics and Physics, University of Science and Technology Beijing, 30 Xueyuan Road, Haidian District, Beijing, 100083
2.
Department of Mathematics, Henan Normal University, Xinxiang, 453007

Received: October 31, 2014

Revised: April 30, 2015

Published: October 2015

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Abstract

In this paper, we study a parabolic type equation involving space integrals on a bounded smooth domain. First, using the Banach fixed point theorem, we establish the well-posedness in Lebesgue spaces. Then, with the help of Nehari functional, we find the threshold of the initial data such that the solution either exists globally or blows up in finite time.

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Mathematics Subject Classification: Primary: 35Kxx; 35K20.

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