Abstract for the talk on 27.04.2018 (11:00 h)

Arbeitsgemeinschaft ANGEWANDTE ANALYSIS

Luca Scarpa (University College London)
Well-posedness of semilinear SPDEs with singular drift: a variational approach

We prove well-posedness for singular semilinear SPDEs on a smooth bounded domain D in n of the form
dX (t)+ AX (t)dt+ β(X(t))dt ∋ B (t,X (t))dW (t),   X(0) = X0.

The linear part is associated to a linear coercive maximal monotone operator A on L2(D), while β is a (multivalued) maximal monotone graph everywhere defined on on which no growth nor smoothness conditions are required. Moreover, the noise is given by a cylindrical Wiener process on a Hilbert space U, with a stochastic integrand B taking values in the Hilbert-Schmidt operators from U to L2(D): classical Lipschitz-continuity hypotheses for the diffusion coefficient are assumed. A comparison with the corresponding deterministic equation and possible generalizations are discussed. This study is based on a joint work with Carlo Marinelli (University College London).

 

29.04.2018, 02:30