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


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.


Boundary Condition Stochastic Process White Noise Probability Theory Mathematical Biology 
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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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