Differential and Integral Equations

A Trotter-type theorem for nonlinear stochastic equations in variational formulation and homogenization

Ioana Ciotir

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This paper is concerned with the nonlinear partial differential equations of calculus of variations perturbed by noise in the Gelfand triple $V\subset H\subset V^{\prime }$. The main result is a Trotter-type theorem for this equation. In the second part of the paper we prove that, if we assume graph convergence of the sequence of nonlinear operators $ \{ A^{\alpha} \} _{\alpha }$, we have convergence of the corresponding sequence of invariant measures. Those results are used in the last part of the paper to study the homogenization problem for the equation, in the case of the differential operator of the type $A ( u ) =- \text{\mathrm {div}} [ a ( \nabla u ) ], $ for $u\in H_{0}^{1} ( \mathcal{O} ).$

Article information

Differential Integral Equations, Volume 24, Number 3/4 (2011), 371-388.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K57: Reaction-diffusion equations 60J60: Diffusion processes [See also 58J65] 35B27: Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50]


Ciotir, Ioana. A Trotter-type theorem for nonlinear stochastic equations in variational formulation and homogenization. Differential Integral Equations 24 (2011), no. 3/4, 371--388. https://projecteuclid.org/euclid.die/1356019037

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