Regularizing the Cauchy Problem for the Heat Equation by Sign Restrictions

Knabner P (1983)

Publication Language: English

Publication Type: Book chapter / Article in edited volumes

Publication year: 1983

Publisher: Birkhäuser

Edited Volumes: Improperly Posed Problems and Their Numerical Treatment

Series: International Series of Numerical Mathematics

City/Town: Basel

Book Volume: 63

Pages Range: 165-177

ISBN: 978-3-0348-5462-7

URI: https://www1.am.uni-erlangen.de/research/publications/Jahr_1983/1983_Kn_RegularizingTheCauchyProblForTheHeatEquatiBySignRestrict

DOI: 10.1007/978-3-0348-5460-3_12

Abstract

We consider the non-characteristic Cauchy problem for the heat equation. For certain a priori information about the solution the amount of regularization, i.e. the behaviour of the module of continuity is investigated. Especially for sign restrictions continuous dependence of Hölder type in the interior is shown. This sharpens a result of Pucci (1959), who did not succeed in estimating the module of continuity. This estimate leads to some conjectures, which fit quite well within the results of numerical case studies.

Authors with CRIS profile

Peter Knabner Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

How to cite

APA:

Knabner, P. (1983). Regularizing the Cauchy Problem for the Heat Equation by Sign Restrictions. In Improperly Posed Problems and Their Numerical Treatment. (pp. 165-177). Basel: Birkhäuser.

MLA:

Knabner, Peter. "Regularizing the Cauchy Problem for the Heat Equation by Sign Restrictions." Improperly Posed Problems and Their Numerical Treatment. Basel: Birkhäuser, 1983. 165-177.

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