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Heat equation with singular potential and singular data

Published online by Cambridge University Press:  12 July 2007

M. Nedeljkov ,
S. Pilipović  and
D. Rajter-Ćirić
M. Nedeljkov
Affiliation:
Department of Mathematics and Informatics, Trg Dositeja Obradovića 5, 21000 Novi Sad, Serbia and Montenegro ([email protected])
S. Pilipović
Affiliation:
Department of Mathematics and Informatics, Trg Dositeja Obradovića 5, 21000 Novi Sad, Serbia and Montenegro ([email protected])
D. Rajter-Ćirić
Affiliation:
Department of Mathematics and Informatics, Trg Dositeja Obradovića 5, 21000 Novi Sad, Serbia and Montenegro ([email protected])
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Abstract

Nets of Schrödinger C0-semigroups (Sε)ε with the polynomial growth with respect to ε are used for solving the Cauchy problem (∂t − Δ)U + VU = f(t, U), U(0, x) = U0(x) in a suitable generalized function algebra (or space), where V and U0 are singular generalized functions while f satisfies a Lipschitz-type condition. The existence of distribution solutions is proved in appropriate cases by the means of white noise calculus as well as classical energy estimates.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 135 , Issue 4 , August 2005 , pp. 863 - 886
Copyright
Copyright © Royal Society of Edinburgh 2005

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