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Zeitschrift für Analysis und ihre Anwendungen


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Volume 35, Issue 2, 2016, pp. 173–180
DOI: 10.4171/ZAA/1560

Published online: 2016-04-13

The Profile of Blow-Up for a Neumann Problem of Nonlocal Nonlinear Diffusion Equation with Reaction

Rong-Nian Wang[1], Zhi-Xue Liu[2] and Yong Zhou[3]

(1) Shanghai Normal University, China
(2) Nanchang University, China
(3) Xiangtan University, Xiangtan, Hunan, China

In this note, we consider a Neumann problem for nonlocal nonlinear diffusion equation with reaction, which may be seen as a significant generalization of the usual Neumann problem for the heat equation. For the blow-up solutions, the blow-up rate estimates and spacial localization of blow-up set are studied.

Keywords: Nonlocal nonlinear diffusion, blow-up rate, blow-up set

Wang Rong-Nian, Liu Zhi-Xue, Zhou Yong: The Profile of Blow-Up for a Neumann Problem of Nonlocal Nonlinear Diffusion Equation with Reaction. Z. Anal. Anwend. 35 (2016), 173-180. doi: 10.4171/ZAA/1560