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Blow-up of solutions to a Dirichlet problem for the discrete semi-linear heat equation
| Content Provider | Semantic Scholar |
|---|---|
| Author | Matsuya, Keisuke |
| Copyright Year | 2012 |
| Abstract | In this paper, the initial and boundary problem of the difference equation which is a discretization of the semi-linear heat equation. The difference equation derived by discretizing the semi-linear heat equation has solutions which show characteristics corresponding to the characteristics of the blow-up solutions for the original equation. The initial and boundary problem for the original equation has blow-up solutions when a certain condition is met. We prove that when a similar condition as that of the original solution is met in the initial and boundary problem for the difference equation, the difference equation has blow-up solutions having characteristics corresponding to the characteristics of the blow-up solutions for the original equation. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://arxiv.org/pdf/1211.1192v1.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
