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Licensed Unlicensed Requires Authentication Published by De Gruyter February 15, 2014

The Cauchy problem for the heat equation with a random right side

  • Yuriy V. Kozachenko EMAIL logo and Anna I. Slyvka-Tylyshchak

Abstract.

In this paper the heat equation with a random right side is examined. In particular, we give conditions for the existence of solutions in the case when the right side is a random field, sample continuous with probability one from the space Lp(Ω). Estimations for the distribution of the supremum of solutions of such equations are found.

MSC: 35K05; 60G15
Received: 2013-06-28
Accepted: 2014-01-16
Published Online: 2014-02-15
Published in Print: 2014-03-01

© 2014 by Walter de Gruyter Berlin/Boston

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