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):
$$ \left\{\begin{array}{l}\frac{\mathrm{d}X(t)}{\mathrm{d}t}= AX(t)+b\left(X(t)\right),\kern1em t\ge 0,\\ {}X(0)=x\in H,\end{array}\right. $$


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

Authors and Affiliations

  1. 1.Scuola Normale SuperiorePisaItaly