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Probability Theory and Related Fields

, Volume 116, Issue 3, pp 421–443 | Cite as

Nonlinear stochastic wave and heat equations

  • Szymon Peszat
  • Jerzy Zabczyk

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.

Keywords

Covariance Wave Equation Heat Equation Nonlinear Wave Wiener Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Szymon Peszat
    • 1
  • Jerzy Zabczyk
    • 2
  1. 1.Institute of Mathematics, Polish Academy of Sciences, Św. Tomasza 30/7, 31-027 Kraków, Poland. e-mail: napeszat@cyf-kr.edu.plPL
  2. 2.Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland. e-mail: zabczyk@@mpan.impan.gov.plPL

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