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Nonlinear stochastic wave and heat equations
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  • Published: March 2000

Nonlinear stochastic wave and heat equations

  • Szymon Peszat1 &
  • Jerzy Zabczyk2 

Probability Theory and Related Fields volume 116, pages 421–443 (2000)Cite this article

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Abstract.

We study nonlinear wave and heat equations on ℝd 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 ℝd-space. We give necessary and sufficient conditions for the existence of a function-valued solution in terms of the covariance kernel of the noise.

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Authors and Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, Św. Tomasza 30/7, 31-027 Kraków, Poland. e-mail: napeszat@cyf-kr.edu.pl, , , , , , PL

    Szymon Peszat

  2. Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland. e-mail: zabczyk@@mpan.impan.gov.pl, , , , , , PL

    Jerzy Zabczyk

Authors
  1. Szymon Peszat
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  2. Jerzy Zabczyk
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Received: 1 April 1998 / Revised version: 23 June 1999 / Published online: 7 February 2000

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Peszat, S., Zabczyk, J. Nonlinear stochastic wave and heat equations. Probab Theory Relat Fields 116, 421–443 (2000). https://doi.org/10.1007/s004400050257

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  • Issue Date: March 2000

  • DOI: https://doi.org/10.1007/s004400050257

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Keywords

  • Covariance
  • Wave Equation
  • Heat Equation
  • Nonlinear Wave
  • Wiener Process
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