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Extinction and positivity of the solutions of the heat equations with absorption on networks

Title
Extinction and positivity of the solutions of the heat equations with absorption on networks
Authors
Chung Y.-S.Lee Y.-S.Chung S.-Y.
Ewha Authors
정윤성
Issue Date
2011
Journal Title
Journal of Mathematical Analysis and Applications
ISSN
0022-247XJCR Link
Citation
vol. 380, no. 2, pp. 642 - 652
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
In this paper, we propose a discrete version of the following semilinear heat equation with absorption ut=δu-uq with q>1, which is said to be the ω- heat equation with absorption on a network. Using the discrete Laplacian operator δω on a weighted graph, we define the ω-heat equations with absorption on networks and give their physical interpretations. The main concern is to investigate the large time behaviors of nontrivial solutions of the equations whose initial data are nonnegative and the boundary data vanish. It is proved that the asymptotic behaviors of the solutions u(x,t) as t tends to +∞ strongly depend on the sign of q-1. © 2011 Elsevier Inc.
DOI
10.1016/j.jmaa.2011.03.006
Appears in Collections:
연구기관 > 수리과학연구소 > Journal papers
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