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Article Dans Une Revue Proceedings of the Royal Society of Edinburgh: Section A, Mathematics Année : 2021

Well-posedness for nonlinear SPDEs with strongly continuous perturbation

Résumé

Abstract We consider the well-posedness of a stochastic evolution problem in a bounded Lipschitz domain D ⊂ ℝ d with homogeneous Dirichlet boundary conditions and an initial condition in L 2 ( D ). The main technical difficulties in proving the result of existence and uniqueness of a solution arise from the nonlinear diffusion-convection operator in divergence form which is given by the sum of a Carathéodory function satisfying p -type growth associated with coercivity assumptions and a Lipschitz continuous perturbation. In particular, we consider the case 1 < p < 2 with an appropriate lower bound on p determined by the space dimension. Another difficulty arises from the fact that the additive stochastic perturbation with values in L 2 ( D ) on the right-hand side of the equation does not inherit the Sobolev spatial regularity from the solution as in the multiplicative noise case.

Dates et versions

hal-04286152 , version 1 (15-11-2023)

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Guy Vallet, Aleksandra Zimmermann. Well-posedness for nonlinear SPDEs with strongly continuous perturbation. Proceedings of the Royal Society of Edinburgh: Section A, Mathematics, 2021, 151 (1), pp.265-295. ⟨10.1017/prm.2020.13⟩. ⟨hal-04286152⟩
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