| Abstract: |
| We consider a doubly nonlinear evolution equation with multiplicative noise and show existence and uniqueness of a strong solution.
Using a semi-implicit time-discretization we first get approximate solutions with monotonicity arguments. We establish a-priori estimates which yield the tightness of the sequence of image measures induced by the sequence of approximate solutions. Using the theroems of Prokhorov and Skorokhod we get a.s. convergence of a subsequence on a new probability space and thereby existence of a martingale solution. Pathwise uniqueness, obtained by an L1-method, allows to show existence and uniqueness of strong solutions. |
|