Related papers: Regularity for evolution equations with non-autono…

We show that paths of solutions to parabolic stochastic differential equations have the same regularity in time as the Wiener process (as of the current state of art). The temporal regularity is considered in the Besov-Orlicz space…

In this paper, the Cauchy problem for linear and nonlinear convolution wave equations are studied.The equation involves convolution terms with a general kernel functions whose Fourier transform are operator functions defined in a Banach…

This paper is devoted to studying stochastic parabolic evolution equations with additive noise in Banach spaces of M-type 2. We construct both strict and mild solutions possessing very strong regularities. First, we consider the linear…

In this paper, we consider the linear evolution equation $dy(t)=Ay(t)dt+Gy(t)dx(t)$, where $A$ is a closed operator, associated to a semigroup, with good smoothing effects in a Banach space $E$, $x$ is a nonsmooth path, which is…

In this paper we obtain a stabilization result for the Schr\"odinger equation under generic assumptions on the potential. Then we consider the Schr\"odinger equation with a potential which has a random time-dependent amplitude. We show that…

A variant of the abstract Cauchy-Kovalevskaya theorem is considered. We prove existence and uniqueness of classical solutions to the nonlinear, non-autonomous initial value problem \[ \frac{du(t)}{dt} = A(t)u(t) + B(u(t),t), \ \ u(0) = x \]…

The paper emphasizes the property of stability for skew-evolution semiflows on Banach spaces, defined by means of evolution semiflows and evolution cocycles and which generalize the concept introduced by us in a previous paper. There are…

We study neural field equations, which are prototypical models of large-scale cortical activity, subject to random data. We view this spatially-extended, nonlocal evolution equation as a Cauchy problem on abstract Banach spaces, with…

Stochastic evolution equations in Banach spaces with unbounded nonlinear drift and diffusion operators driven by a finite dimensional Brownian motion are considered. Under some regularity condition assumed for the solution, the rate of…

In this paper, we consider a non-autonomous nonlinear evolution equation in separable, reflexive Banach spaces. First, we consider a linear problem and establish the approximate controllability results by finding a feedback control with the…

A strong inspiration for studying perturbation theory for fractional evolution equations comes from the fact that they have proven to be useful tools in modeling many physical processes. In this paper, we study fractional evolution…

For nonuniform exponentially bounded evolution families defined on Banach spaces, we introduce a class of Banach function spaces, whose norms are completely determined by the nonuniform behaviour of the corresponding evolution family. We…

Results of a previous paper [Commun. Contemp. Math., 09 (2007) 217-251] on the existence of solutions to a nonlinear evolution equation in an abstract Lebesgue space, arising from kinetic theory, are re-obtained in the more general setting…

In this paper we deal with a nonlinear Schr\"{o}dinger equation with chaotic, random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton evolution, with the strength of the nonlinearity perturbed in the space and time…

We study existence, uniqueness, and a limiting behaviour of solutions to an abstract linear evolution equation in a scale of Banach spaces. The generator of the equation is a perturbation of the operator which satisfies the classical…

We consider parabolic nonlocal Venttsel' problems in polygonal and piecewise smooth two-dimensional domains and study existence, uniqueness and regularity in (anisotropic) weighted Sobolev spaces of the solution.

In this work, we study the regularity of positive solutions for nonlinear fractional differential equation with a singular weight. We define the new Banach space and use this space to show the regularity. We also give an example with a…

The initial-boundary value problems for linear non-autonomous first order evolution equations are examined. Our assumptions provide a unified treatment which is applicable to many situations, where the domains of the operators may change…

We study the extragradient method for solving vector quasi-equilibrium problems in Banach spaces, which generalizes the extragradient method for vector equilibrium problems and scalar quasi-equilibrium problems. We propose a regularization…

Here we consider a perturbation of continuous mappings on Banach spaces and investigate their image under various conditions. Consequently, we study the solvability of some classes of equations and inclusions. For these, we start by the…