## On the Cauchy problem for the one-dimensional heat equation

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**17**(1963), 257-269 Request permission

## 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.

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## Additional Information

- © Copyright 1963 American Mathematical Society
- Journal: Math. Comp.
**17**(1963), 257-269 - MSC: Primary 35.78
- DOI: https://doi.org/10.1090/S0025-5718-1963-0162064-8
- MathSciNet review: 0162064