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Long time existence for the heat equation with a noise term
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  • Published: December 1991

Long time existence for the heat equation with a noise term

  • Carl Mueller1 

Probability Theory and Related Fields volume 90, pages 505–517 (1991)Cite this article

  • 309 Accesses

  • 35 Citations

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Summary

We consider the equationu t =u xx +u γ W forx on a finite interval, with Dirichlet boundary conditions. W is spacetime white noise. The initial condition is continuous and nonnegative. We show existence and uniqueness for all time, provided 1 ≧γ<3/2.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Rochester, 14627, Rochester, NY, USA

    Carl Mueller

Authors
  1. Carl Mueller
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Supported by an NSF grant

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Cite this article

Mueller, C. Long time existence for the heat equation with a noise term. Probab. Th. Rel. Fields 90, 505–517 (1991). https://doi.org/10.1007/BF01192141

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  • Received: 21 June 1990

  • Revised: 31 July 1991

  • Issue Date: December 1991

  • DOI: https://doi.org/10.1007/BF01192141

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Keywords

  • Boundary Condition
  • Stochastic Process
  • White Noise
  • Probability Theory
  • Mathematical Biology
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