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math.PR2025
A mild rough Gronwall Lemma with applications to non-autonomous evolution equations
Alexandra Blessing, Mazyar Ghani Varzaneh, Tim Seitz
We derive a Gronwall type inequality for mild solutions of non-autonomous parabolic rough partial differential equations (RPDEs). This inequality together with an analysis of the C…
math.PR2025
Pathwise mild solutions for superlinear stochastic evolution equations and their attractors
Alexandra Blessing, Tim Seitz, Stefanie Sonner +1
We investigate stochastic parabolic evolution equations with time-dependent random generators and locally Lipschitz continuous drift terms. Using pathwise mild solutions, we constr…
math.PR2024
Existence and regularity of random attractors for stochastic evolution equations driven by rough noise
Alexandra Neamtu, Tim Seitz
This work establishes the existence and regularity of random pullback attractors for parabolic partial differential equations with rough nonlinear multiplicative noise under natura…