Intermittence and nonlinear parabolic stochastic partial differential equations

  title={Intermittence and nonlinear parabolic stochastic partial differential equations},
  author={Mohammud Foondun Davar Khoshnevisan},
  • 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
Highly Influential
This paper has highly influenced 12 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS
Highly Cited
This paper has 38 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.


Publications citing this paper.


Publications referenced by this paper.
Showing 1-10 of 44 references

An Introduction to Stochastic Partial Differential Equations

  • Walsh, B John
  • in: École d’été de probabilités de Saint…
  • 1986
Highly Influential
6 Excerpts

On the support of solutions to the heat equation with noise, Stochastics and Stochastics Rep

  • Mueller, Carl
  • 1991
Highly Influential
5 Excerpts

On phase transitions and limit theorems for homopolymers

  • M. Cranston, S. Molchanov
  • in: Probability and Mathematical Physics, CRM…
  • 2007
Highly Influential
5 Excerpts

Some non-linear S.P.D.E.’s that are second order in time, Electron

  • Dalang, C Robert, Carl Mueller
  • J. Probab. 8,
  • 2003
Highly Influential
3 Excerpts

Nonlinear stochastic wave and heat equations, Probab

  • Peszat, Szymon, Jerzy Zabczyk
  • Th. Rel. Fields 116(3),
  • 2000
Highly Influential
5 Excerpts

Extending the martingale measure stochastic integral with applications to spatially homogeneous s.p.d.e.’s

  • Dalang, C Robert
  • Electron. J. Probab. 4,
  • 1999
Highly Influential
4 Excerpts

Parabolic Anderson Problem and Intermittency

  • Carmona, A René, S. A. Molchanov
  • Memoires of the Amer. Math. Soc
  • 1994
Highly Influential
7 Excerpts

The stochastic heat equation: Feynman–Kac formula and intermittence

  • Bertini, Lorenzo, Nicoletta Cancrini
  • J. Statist. Physics 78(5/6),
  • 1994
Highly Influential
6 Excerpts

Stochastic Equations in Infinite Dimensions

  • Da Prato, Giuseppe, Jerzy Zabczyk
  • 1992
Highly Influential
5 Excerpts

Similar Papers

Loading similar papers…