相关论文: On approximate solutions of semilinear evolution e…

The current article examines the approximate controllability problem for non-instantaneous impulsive fractional evolution equations of order $1<\alpha<2$ with state-dependent delay in separable reflexive Banach spaces. In order to establish…

We present a new proof of well-posedness of stochastic evolution equations in variational form, relying solely on a (nonlinear) infinite-dimensional approximation procedure rather than on classical finite-dimensional projection arguments of…

We consider a semilinear parabolic equation with a large class of nonlinearities without any growth conditions. We discretize the problem with a discontinuous Galerkin scheme dG(0) in time (which is a variant of the implicit Euler scheme)…

In this note we provide a self-contained proof of an existence and uniqueness result for a class of Banach space valued evolution equations with an additive forcing term. The framework of our abstract result includes, for example, finite…

In this paper, we investigate the existence and uniqueness of mild and strong solutions of fractional semilinear evolution equations in the Hilfer sense, by means of Banach fixed point theorem and the Gronwall inequality.

We consider the Shallow Water equations in the supercritical and subcritical cases in one space variable,posed in a finite spatial interval with characteristic boundary conditions at the endpoints, which, as is well known, are…

In this paper, using the subvariant functional method due to Favard \cite{Favard}, we prove the existence of aunique compact almost automorphic solution for a class of semilinear evolution equations in Banach spaces. More specifically, we…

This work is devoted to the study of a nonlocal-in-time evolutional problem for the first order differential equation in Banach space. Our primary approach, although stems from the convenient technique based on the reduction of a nonlocal…

We resolve a longstanding open problem in the computational modeling of nonlinear plates by introducing a numerical method that exactly enforces the isometry constraint, namely, that the first fundamental form of the mid-surface coincides…

This paper is concerned with the approximation of solutions to a class of second order non linear abstract differential equations. The finite-dimensional approximate solutions of the given system are built with the aid of the projection…

This paper investigates the existence and uniqueness of solutions for a nonlinear evolution equation governed by an m-accretive operator A in a Banach space, presenting a perturbation term that does not satisfy the Lipschitz condition.

We study both strict and mild solutions to parabolic evolution equations of the form $dX+AXdt=F(t)dt+G(t)dW(t)$ in Banach spaces. First, we explore the deterministic case. The maximal regularity of solutions has been shown. Second, we…

In this paper we consider Galerkin-finite element methods that approximate the solutions of initial-boundary-value problems in one space dimension for parabolic and Schr\"odinger evolution equations with dynamical boundary conditions. Error…

We study the convergence of semilinear parabolic stochastic evolution equations, posed on a sequence of Banach spaces approximating a limiting space and driven by additive white noise projected onto the former spaces. Under appropriate…

The work is organized as follows. First an introduction is given in Chapter 1. In Chapter 2 we introduce the POD method in finite and infinite-dimensional Hilbert spaces and discuss various applications. Chapter 3 is devoted to to POD-based…

We survey some representative results on fuzzy fractional differential equations, controllability, approximate controllability, optimal control, and optimal feedback control for several different kinds of fractional evolution equations.…

This paper studies Galerkin approximations applied to the Zakai equation of stochastic filtering. The basic idea of this approach is to project the infinite-dimensional Zakai equation onto some finite-dimensional subspace generated by…

We provide an accurate verification method for solutions of heat equations with a superlinear nonlinearity. The verification method numerically proves the existence and local uniqueness of the exact solution in a neighborhood of a…

These lecture notes introduce the Galerkin method to approximate solutions to partial differential and integral equations. We begin with some analysis background to introduce this method in a Hilbert Space setting, and subsequently…

This paper investigates the controllability of systems governed by conformable fractional order derivatives. It first establishes the existence and uniqueness of evolution operators for non-autonomous fractional-order homogeneous systems,…