Blow-up of solutions for the heat equations with variable source on graphs
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Authors
Qiao Xin
- College of Mathematics and Statistics, Yili Normal University, 835000 Yining, P. R. China.
Dengming Liu
- School of Mathematics and Computational Science, Hunan University of Science and Technology, 411201 Xiangtan, P. R. China.
Abstract
In this paper, we mainly consider the blow-up problem for the discrete heat equations with variable
source on finite graphs
\[u_t = \Delta_\omega u + u^{p(x)}\]
with homogeneous Dirichlet boundary conditions and positive initial energy. We prove that the corresponding solutions blow up at a finite time with large enough initial data. Moreover, the blow-up rate is also
considered.
Share and Cite
ISRP Style
Qiao Xin, Dengming Liu, Blow-up of solutions for the heat equations with variable source on graphs, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 4, 1685--1692
AMA Style
Xin Qiao, Liu Dengming, Blow-up of solutions for the heat equations with variable source on graphs. J. Nonlinear Sci. Appl. (2016); 9(4):1685--1692
Chicago/Turabian Style
Xin, Qiao, Liu, Dengming. "Blow-up of solutions for the heat equations with variable source on graphs." Journal of Nonlinear Sciences and Applications, 9, no. 4 (2016): 1685--1692
Keywords
- Blow-up
- discrete heat equation
- variable reaction
- finite graphs.
MSC
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