Nonlinear stochastic wave and heat equations |
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| Authors: | Szymon Peszat Jerzy Zabczyk |
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| Institution: | (1) Institute of Mathematics, Polish Academy of Sciences, Św. Tomasza 30/7, 31-027 Kraków, Poland. e-mail: napeszat@cyf-kr.edu.pl, PL;(2) Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland. e-mail: zabczyk@@mpan.impan.gov.pl, PL |
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| Abstract: | We study nonlinear wave and heat equations on ℝ
d
driven by a spatially homogeneous Wiener process. For the wave equation we consider the cases of d = 1, 2, 3. The heat equation is considered on an arbitrary ℝ
d
-space. We give necessary and sufficient conditions for the existence of a function-valued solution in terms of the covariance
kernel of the noise.
Received: 1 April 1998 / Revised version: 23 June 1999 / Published online: 7 February 2000 |
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