Intermittence and nonlinear parabolic stochastic partial differential equations

@inproceedings{Khoshnevisan2008IntermittenceAN,
  title={Intermittence and nonlinear parabolic stochastic partial differential equations},
  author={Mohammud Foondun Davar Khoshnevisan},
  year={2008}
}
  • Mohammud Foondun Davar Khoshnevisan
  • Published 2008
We consider nonlinear parabolic SPDEs of the form ∂tu=L u+σ(u)ẇ, where ẇ denotes spacetime white noise, σ : R→ R is [globally] Lipschitz continuous, and L is the L2-generator of a Lévy process. We present precise criteria for existence as well as uniqueness of solutions. More significantly, we prove that these solutions grow in time with at most a precise exponential rate. We establish also that when σ is globally Lipschitz and asymptotically sublinear, the solution to the nonlinear heat… CONTINUE READING
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