Related papers: An order approach to SPDEs with antimonotone terms

We consider a linear algebra approach to establishing a discrete comparison principle for a nonmonotone class of quasilinear elliptic partial differential equations. In the absence of a lower order term, we require local conditions on the…

In this paper, we provide a direct approach to the existence and uniqueness of strong (in the probabilistic sense) and weak (in the PDE sense) solutions to quasilinear stochastic partial differential equations, which are neither monotone…

In this note we provide conditions for local invariance of finite dimensional submanifolds for solutions to stochastic partial differential equations (SPDEs) in the framework of the variational approach. For this purpose, we provide a…

Uniqueness of the finite element solution for nonmonotone quasilinear problems of elliptic type is established in one and two dimensions. In each case, we prove a comparison theorem based on locally bounding the variation of the discrete…

In this paper, we use the variational approach to investigate recurrent properties of solutions for stochastic partial differential equations, which is in contrast to the previous semigroup framework. Consider stochastic differential…

Systems of parabolic, possibly degenerate parabolic SPDEs are considered. Existence and uniqueness are established in Sobolev spaces. Similar results are obtained for a class of equations generalizing the deterministic first order symmetric…

We survey some of our recent results on existence, uniqueness and regularity of function solutions to parabolic and transport type partial differential equations driven by non-differentiable noises. When applied pathwise to random…

We consider a quasilinear elliptic equation involving a first order term, under zero Dirichlet boundary condition in half spaces. We prove that any positive solution is monotone increasing w.r.t. the direction orthogonal to the boundary.…

In this paper, we first prove existence and uniqueness of the solution of a backward doubly stochastic differential equation (BDSDE) and of the related stochastic partial differential equation (SPDE) under monotonicity assumption on the…

By means of a recent variational technique, we prove the existence of radially monotone solutions to a class of nonlinear problems involving the $p$-Laplace operator. No subcriticality condition (in the sense of Sobolev spaces) is required.

This article is devoted to the analysis of semilinear, parabolic, Stochastic Partial Differential Equations, with slow and fast time scales. Asymptotically, an averaging principle holds: the slow component converges to the solution of…

We establish the existence of weak solutions of coupled systems of elliptic partial differential equations with quasimonotone nonlinearities in the domain interior and on the boundary. When the nonlinearities satisfy some monotonicity…

The Monotonicity inequality is an important tool in the understanding of existence and uniqueness of strong solutions for Stochastic PDEs. In this article, we discuss three approaches to establish this deterministic inequality explicitly.

We study linear backward stochastic partial differential equations of parabolic type with special boundary condition that connect the terminal value of the solution with a functional over the entire past solution. Uniqueness, solvability…

We study function-valued solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable parabolicity hypotheses. We provide…

We prove existence and uniqueness of strong solutions, as well as continuous dependence on the initial datum, for a class of fully nonlinear second-order stochastic PDEs with drift in divergence form. Due to rather general assumptions on…

This paper extends deterministic notions of Strong Stability Preservation (SSP) to the stochastic setting, enabling nonlinearly stable numerical solutions to stochastic differential equations (SDEs) and stochastic partial differential…

We investigate the periodic and stationary solutions of distribution-dependent stochastic differential equations. While generally, the semigroups associated with the equations are nonlinear, we show that the methods of weak convergence and…

A nonlinear fourth-order parabolic equation in one space dimension with periodic boundary conditions is studied. This equation arises in the context of fluctuations of a stationary nonequilibrium interface and in the modeling of quantum…

Parameter estimation for a parabolic linear stochastic partial differential equation in one space dimension is studied observing the solution field on a discrete grid in a fixed bounded domain. Considering an infill asymptotic regime in…