Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Nonlinear Stochastic Partial Differential Equations

  • Giuseppe Da Prato
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_367-3

Definition of the Subject

Several nonlinear partial differential evolution equations can be written as abstract equations in a suitable Hilbert space H (we shall denote by | ⋅ | the norm and by ⟨⋅,⋅⟩ the scalar product in H) of the following form (Temam 1988):
$$ \left\{\begin{array}{l}\frac{\mathrm{d}X(t)}{\mathrm{d}t}= AX(t)+b\left(X(t)\right),\kern1em t\ge 0,\\ {}X(0)=x\in H,\end{array}\right. $$

Keywords

Invariant Measure Mild Solution Burger Equation Multiplicative Noise Continuous Semigroup 
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 Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Scuola Normale SuperiorePisaItaly