Related papers: A stochastic Datko-Pazy theorem

We consider the Cauchy problem for stochastic fractional evolution equations with Caputo time fractional derivative of order $1<\alpha<2$ and space variable coefficients on an unbounded domain. The space derivatives that appear in the…

We consider a stochastic parabolic partial differential equation with Dirichlet boundary conditions, multiplicative stochastic noise, and a monotone parabolic operator A. The growth and coercivity of A is controlled by a general N-function…

In this paper we give a criterion to prove boundedness results for several operators from $H^1((0,\infty),\gamma_\alpha)$ to $L^1((0,\infty),\gamma_\alpha)$ and also from $L^\infty((0,\infty),\gamma_\alpha)$ to…

Let E be a type 2 UMD Banach space, H a Hilbert space and let p be in [1,\infty). Consider the following stochastic delay equation in E: dX(t) = AX(t) + CX_t + b(X(t),X_t)dW_H(t), t>0; X(0) = x_0; X_0 = f_0. Here A : D(A) -> E is the…

In this paper we study $R$-boundedness of operator families $\mathcal{T}\subset \calL(X,Y)$, where $X$ and $Y$ are Banach spaces. Under cotype and type assumptions on $X$ and $Y$ we give sufficient conditions for $R$-boundedness. In the…

We prove spectral multiplier theorems for H\"ormander classes $\mathcal{H}^\alpha\_p$ for 0-sectorial operators A on Banach spaces assuming a bounded $H^\infty(\Sigma\_\sigma)$ calculus for some $\sigma \in (0,\pi)$ and norm and certain…

We consider Cauchy problem for a divergence form second order parabolic operator with rapidly oscillating coefficients that are periodic in spatial variable and random stationary ergodic in time. As was proved in [25] and [13] in this case…

Let $\Gamma$ be a graph with the doubling property for the volume of balls and $P$ a reversible random walk on $\Gamma$. We introduce $H^1$ Hardy spaces of functions and $1$-forms adapted to $P$ and prove various characterizations of these…

We consider the perturbation of parabolic operators of the form $\partial_t+P(x,D)$ by large-amplitude highly oscillatory spatially dependent potentials modeled as Gaussian random fields. The amplitude of the potential is chosen so that the…

A problem of Banach asks whether every infinite-dimensional Banach space which is isomorphic to all its infinite-dimensional subspaces must be isomorphic to a separable Hilbert space. In this paper we prove a result of a Ramsey-theoretic…

The Riemann-Hilbert (RH) approach, whose origins can be traced back to Riemann's PhD thesis, is well known to be far-reaching. It provides a general framework for expressing solutions of integrable problems such as ODEs or PDEs. Its…

Truncated Riesz spaces was first introduced by Fremlin in the context of real-valued functions. An appropriate axiomatization of the concept was given by Ball. Keeping only the first Ball's Axiom (among three) as a definition of truncated…

We extend the theory of operator-valued frames (resp. bases), hence the theory of frames (resp. bases), for Hilbert spaces and Hilbert C*-modules, in two folds. This extension leads us to develop the theory of operator-valued frames (resp.…

We derive lower bounds on the resolvent operator for the linearized steady Boltzmann equation over weighted L1 Banach spaces in velocity, comparable to those derived by Pogan & Zumbrun in an analogous weighted L2 Hilbert space setting.…

This paper is concerned with solution in H\"{o}lder spaces of the Cauchy problem for linear and semi-linear backward stochastic partial differential equations (BSPDEs) of super-parabolic type. The pair of unknown variables are viewed as…

In this paper, we investigate an inverse Cauchy problem for a stochastic hyperbolic equation. A Lipschitz type observability estimate is established using a pointwise Carleman identity. By minimizing the constructed Tikhonov-type…

The main purpose of this paper is to give an upper bound of Hausdorff dimension of random attractors for a stochastic delayed parabolic equation in Banach spaces. The estimation of dimensions of random attractors are obtained by combining…

We investigate the well-posedness of a class of stochastic second-order in time damped evolution equations in Hilbert spaces, subject to the constraint that the solution lie within the unitary sphere. Then, we focus on a specific example,…

In this paper, we investigate an ill-posed Cauchy problem involving a stochastic parabolic equation. We first establish a Carleman estimate for this equation. Leveraging this estimate, we derive the conditional stability and convergence…

We provide very mild sufficient conditions for space-time domains (non-necessarily cylindrical) which ensure that the continuous Dirichlet problem and the H\"older Dirichlet problem are well-posed, for any parabolic operator in divergence…