Stochastic Volterra equations driven by cylindrical Wiener process

In this paper, stochastic Volterra equations driven by cylindrical Wiener process in Hilbert space are investigated. Sufficient conditions for existence of strong solutions are given. The key role is played by convergence of $\alpha$-times resolvent families.Comment: 14 pages. Sufficient conditions for existence of strong solutions for stochastic fractional Volterra equations are given. Some proofs precise

Well-posedness for a fourth-order equation of Moore-Gibson-Thompson type

In this paper, we completely characterize, only in terms of the data, the well-posedness of a fourth order abstract evolution equation arising from the Moore– Gibson–Thomson equation with memory. This characterization is obtained in the scales of vector-valued Lebesgue, Besov and Triebel–Lizorkin function spaces. Our characterization is flexible enough to admit as examples the Laplacian and the fractional Laplacian operators, among others. We also provide a practical and general criteria that allows L p–L q -well-posedness

Discrete maximal regularity for Volterra equations and nonlocal time-stepping schemes

[EN] In this paper we investigate conditions for maximal regularity of Volterra equations defined on the Lebesgue space of sequences l(p)(Z) by using Blunck's theorem on the equivalence between operator-valued l(p)-multipliers and the notion of R-boundedness. We show sufficient conditions for maximal l(p) - l(q) regularity of solutions of such problems solely in terms of the data. We also explain the significance of kernel sequences in the theory of viscoelasticity, establishing a new and surprising connection with schemes of approximation of fractional models.The first author was partially supported by FONDECYT, Grant No 1180041. The second author was supported by MEC, grant MTM2016-75963-P and GVA/2018/110.Lizama, C.; Murillo Arcila, M. (2020). Discrete maximal regularity for Volterra equations and nonlocal time-stepping schemes. Discrete and Continuous Dynamical Systems. 40(1):509-528. https://doi.org/10.3934/dcds.2020020S50952840