相关论文: On evolution equations with white-noise boundary c…

In this paper, we study the existence of solution for stochastic evolution equations with almost sectorial operators and possibly a non dense domain. Such problems cover several types of evolution equations, we are interested here in…

We study the well solvability of nonlinear backward stochastic evolutionary equations driven by a space-time white noise. We first establish a novel a priori estimate for solution of linear backward stochastic evolutionary equations, and…

We show that that the stochastic 3D primitive equations with either the physical boundary conditions or Neumann boundary conditions on the top and bottom and Dirichlet boundary condition on the sides driven by multiplicative…

The aim of this article is to propose a systematic study of transparent boundary conditions for finite difference approximations of evolution equations. We try to keep the discussion at the highest level of generality in order to apply the…

In this paper, we develop a way of analyzing the random dynamics of stochastic evolution equations with a non-dense domain. Such problems cover several types of evolution equations. We are particularly interested in evolution equations with…

In this paper, our main goal is to study the evolution problem associated with the Laplacian operator with Dirichlet boundary conditions on a regular tree. To this end, we place special emphasis on the associated first eigenvalue problem,…

In this note we develop a framework which allows to prove an existence result for non-linear evolution problems involving time-dependent, pseudo-monotone operators. This abstract existence result is applicable to a large class of concrete…

In the Cauchy problem of general relativity one considers initial data that satisfies certain constraints. The evolution equations guarantee that the evolved variables will satisfy the constraints at later instants of time. This is only…

New boundary conditions are constructed and tested numerically for a general first-order form of the Einstein evolution system. These conditions prevent constraint violations from entering the computational domain through timelike…

A class of evolutionary operator equations is studied. As an application the equations of linear acoustics are considered with complex material laws. A dynamic boundary condition is imposed which in the time-harmonic case corresponds to an…

In this paper we study the Poisson and heat equations on bounded and unbounded domains with smooth boundary with random Dirichlet boundary conditions. The main novelty of this work is a convenient framework for the analysis of such…

In this note we present a framework which allows to prove an abstract existence result for evolution equations with pseudo-monotone operators. The assumptions on the spaces and the operators can be easily verified in concrete examples.

The resolution of a very large class of linear and non-linear, stationary and evolutive partial differential problems in the half-space (or similar) under the slip boundary condition is reduced here to that of the corresponding results for…

In this note we develop a framework which allows to prove an abstract existence result for non-linear evolution equations involving so-called non-induced operators, i.e., operators which are not prescribed by a time-dependent family of…

This paper is concerned with an evolution problem having an elliptic equation involving the 1-Laplacian operator and a dynamical boundary condition. We apply nonlinear semigroup theory to obtain existence and uniqueness results as well as a…

We investigate the pathwise well-posedness of stochastic evolution equations perturbed by multiplicative Neumann boundary noise, such as fractional Brownian motion for $H\in(1/3,1/2]$. Combining the controlled rough path approach with the…

We discuss the initial-boundary value problem for the Baumgarte-Shapiro-Shibata-Nakamura evolution system of Einstein's field equations which has been used extensively in numerical simulations of binary black holes and neutron stars. We…

This study investigates Dirichlet boundary condition related to a class of nonlinear parabolic problem with nonnegative $L^1$-data, which has a variable-order fractional $p$-Laplacian operator. The existence and uniqueness of renormalized…

We consider second-order evolution equations in an abstract setting with intermittently delayed/ not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, improving and generalising our previous results…

We prove existence and uniqueness of mild and generalized solutions for a class of stochastic semilinear evolution equations driven by additive Wiener and Poisson noise. The non-linear drift term is supposed to be the evaluation operator…