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On the Cauchy Problem for the One-Dimensional Heat Equation
| Content Provider | Semantic Scholar |
|---|---|
| Author | Ginsberg, Frances |
| Copyright Year | 2010 |
| Abstract | Abstract. In this paper we show that the Cauchy problem for the one-dimensional heat equation, though non-well posed in the sense of Hadamard, can be solved numerically. It is shown that if we admit as solutions functions for which an a priori bound is assumed in some finite rectangle in x — t space then the solution depends Holder continuously upon the given Cauchy data. The specific numerical scheme developed also exhibits the Holder continuity so that we are sure of a meaningful numerical method. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.ams.org/journals/mcom/1963-17-083/S0025-5718-1963-0162064-8/S0025-5718-1963-0162064-8.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Assumed Business continuity Exhibits as Topic Holder Device Component Numerical method Scott continuity |
| Content Type | Text |
| Resource Type | Article |
