Research Communication | Open Access
Volume 2021 | Communication ID 73
Volume 2021 | Communication ID 73
| Well-posedness of stochastic evolution equations under non-linear Miyadera-Voigt perturbations |
Mohamed Fkirine, Said Hadd
Received |
Accepted |
Published |
January 26, 2021 |
February 15, 2021 |
March 15, 2021 |
Abstract: In this talk, we study well-posedness of a class of semi-linear abstract stochastic evolution equations in a Hilbert space H. Here the non-linear term is a function G = F ◦P , where F : H \to H is a Lipschitz function while P : D(P ) ⊂ H \to H is a linear unbounded operator on H. The fact that G is not a Lipschitz function offers many difficulties in applying the usual methods of perturbation in stochastic analysis and thus makes the study interesting. Our approach is new and it is based on admissible observation operators, and allows us to introduce a new concept of solutions ...