A note on maximal estimates for stochastic convolutions

In stochastic partial differential equations it is important to have pathwise regularity properties of stochastic convolutions. In this note we present a new sufficient condition for the pathwise continuity of stochastic convolutions in Banach spaces.Comment: Minor correction

Cα-regularity for nonautonomous linear integro-differential equations of parabolic type

AbstractLinear integrodifferential equations in general Banach space are studied and applications are given to linear integrodifferential partial differential equations

Identifying a BV-kernel in an hyperbolic integrodifferential equation

This paper is devoted to determining the scalar relaxation kernel a in a second-order (in time) integrodifferential equation related to a Banach space when an additional measurement involving the state function is available. A result concerning global existence and uniqueness is proved. The novelty of this paper consists in looking for the kernel a in the Banach space BV (0, T), consisting of functions of bounded variations, instead of the space W1,1(0, T) used up to now to identify a. An application is given, in the framework of L2-spaces, to the case of hyperbolic second-order integrodifferential equations endowed with initial and Dirichlet boundary conditions

Regularity and identification for an integrodifferential one-dimensional hyperbolic equation

In this paper we determine a (possibly) non-continuous scalar relaxation kernel of bounded variation in an integrodifferential equation related to a Banach space when a nonlocal additional measurement involving the state function is available. We prove a result concerning global existence and uniqueness. An application is given, in the framework of space of continuous functions, to the case of one-dimensional hyperbolic second-order integrodifferential equations endowed with initial and Dirichlet boundary conditions