A variational approach to dissipative SPDEs with singular drift. (English) Zbl 1454.60097
Summary: We prove global well-posedness for a class of dissipative semilinear stochastic evolution equations with singular drift and multiplicative Wiener noise. In particular, the nonlinear term in the drift is the superposition operator associated to a maximal monotone graph everywhere defined on the real line, on which neither continuity nor growth assumptions are imposed. The hypotheses on the diffusion coefficient are also very general, in the sense that the noise does not need to take values in spaces of continuous, or bounded, functions in space and time. Our approach combines variational techniques with a priori estimates, both pathwise and in expectation, on solutions to regularized equations.
MSC:
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 47H06 | Nonlinear accretive operators, dissipative operators, etc. |
| 46N30 | Applications of functional analysis in probability theory and statistics |
Keywords:
stochastic evolution equations; singular drift; variational approach; well-posedness; multiplicative noise; monotone operatorsReferences:
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