Strong solutions of semilinear SPDEs with unbounded diffusion - Sorbonne Université
Article Dans Une Revue Stochastics and Partial Differential Equations: Analysis and Computations Année : 2021

Strong solutions of semilinear SPDEs with unbounded diffusion

Résumé

We prove a modification to the classical maximal inequality for stochastic convolutions in 2-smooth Banach spaces using the factorization method. This permits to study semilinear stochastic partial differential equations with unbounded diffusion operators driven by cylindrical Brownian motion via the mild solution approach. In the case of finite dimensional driving noise, provided sufficient regularity on the coefficients, we establish existence and uniqueness of strong solutions. In the case of "critical unboundedness", we show how to use the stochastic compactness method to obtain a martingale solution.
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Dates et versions

hal-03420524 , version 1 (09-11-2021)

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Florian Bechtold. Strong solutions of semilinear SPDEs with unbounded diffusion. Stochastics and Partial Differential Equations: Analysis and Computations, 2021, ⟨10.1007/s40072-021-00216-8⟩. ⟨hal-03420524⟩
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