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Existence and uniqueness results for a non linear stochastic partial differential equation

Part of the Lecture Notes in Mathematics book series (LNM,volume 1236)

Abstract

We study the non linear stochastic partial differential equation \(du(t,x) = A(x,u,Du,D''u)dt + (\sum\limits_{j = 1}^n {G_j (x)D_j u(t,x) + h(x,u(t,x))dW(t)} \)where A is a convex functional and W(t) a real Wiener process. We study the corresponding non linear robust equation by linearization methods. We also prove some existence and uniqueness results for parabolic equations with unbounded coefficients in Hölder spaces.

Keywords

  • Parabolic Equation
  • Uniqueness Result
  • General Elliptic
  • Analytic Semigroup
  • Stochastic Partial Differential Equation

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.

The A.A. are members of G.N.A.F.A. (C.N.R.). This work is partially supported by the Research Funds of the Ministero della Pubblica Istruzione

The A. is presently on duty at Stato Maggiore Marina, Palazzo Marina, Rome

This A. held the present communication at Trento

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© 1987 Springer-Verlag

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Cannarsa, P., Vespri, V. (1987). Existence and uniqueness results for a non linear stochastic partial differential equation. In: Da Prato, G., Tubaro, L. (eds) Stochastic Partial Differential Equations and Applications. Lecture Notes in Mathematics, vol 1236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072880

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  • DOI: https://doi.org/10.1007/BFb0072880

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17211-6

  • Online ISBN: 978-3-540-47408-1

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