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Probability Theory and Related Fields

, Volume 90, Issue 4, pp 505–517 | Cite as

Long time existence for the heat equation with a noise term

  • Carl Mueller
Article

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.

Keywords

Boundary Condition Stochastic Process White Noise Probability Theory Mathematical Biology 
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 1991

Authors and Affiliations

  • Carl Mueller
    • 1
  1. 1.Department of MathematicsUniversity of RochesterRochesterUSA

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