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On the Cauchy problem for the one-dimensional heat equation


Author: F. Ginsberg
Journal: Math. Comp. 17 (1963), 257-269
MSC: Primary 35.78
MathSciNet review: 0162064
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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 Hölder continuously upon the given Cauchy data. The specific numerical scheme developed also exhibits the Hölder continuity so that we are sure of a meaningful numerical method.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1963-0162064-8
Article copyright: © Copyright 1963 American Mathematical Society