Related papers: A note on stochastic semilinear dissipative evolut…
Consider the stochastic evolution equation in a separable Hilbert space with a nice multiplicative noise and a locally Dini continuous drift. We prove that for any initial data the equation has a unique (possibly explosive) mild solution.…
In this paper, we study a semilinear SPDE with a linear Young drift $du_{t}=Lu_{t}dt+f\left(t, u_{t}\right)dt+\left(G_{t}u_{t}+g_{t}\right)d\eta_{t}+h\left(t, u_{t}\right)dW_{t}$, where $L$ is the generator of an analytical semigroup,…
We consider semilinear stochastic evolution equations on Hilbert spaces with multiplicative Wiener noise and linear drift term of the type $A + \varepsilon G$, with $A$ and $G$ maximal monotone operators and $\varepsilon$ a "small"…
We demonstrate the large deviation property for the mild solutions of stochastic evolution equations with monotone nonlinearity and multiplica- tive noise. This is achieved using the recently developed weak convergence method, in studying…
We study the wellposedness and pathwise regularity of semilinear non-autonomous parabolic evolution equations with boundary and interior noise in an $L^p$ setting. We obtain existence and uniqueness of mild and weak solutions. The boundary…
We study a class of stochastic evolution equations with a dissipative forcing nonlinearity and additive noise. The noise is assumed to satisfy rather general assumptions about the form of the covariance function; our framework covers…
We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations with a polynomially growing quasi-monotone nonlinearity and multiplicative Poisson noise. We also study existence and uniqueness of…
We provide an existence and uniqueness result for mild solutions to semilinear stochastic partial differential equations in the framework of the semigroup approach with locally monotone coefficients. An important component of the proof is…
This paper addresses the existence of nonnegative mild solutions for stochastic evolution inclusions through a weak topology approach. Precisely, the study focuses on stochastic evolution inclusions characterized by multivalued…
In this paper, we investigate a semilinear stochastic parabolic equation with a linear rough term $du_{t}=\left[L_{t}u_{t}+f\left(t, u_{t}\right)\right]dt+\left(G_{t}u_{t}+g_{t}\right)d\mathbf{X}_{t}+h\left(t, u_{t}\right)dW_{t}$, where…
We consider a class of semilinear stochastic evolution equations driven by an additive cylindrical stable noise.We investigate structural properties of the solutions like Markov, irreducibility, stochastic continuity, Feller and strong…
The main objective of this work is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see's) and stochastic partial differential equations (spde's) near stationary solutions. Such…
Motivated by the work of T.E. Govindan in [5,8,9], this paper is concerned with a more general semilinear stochastic evolution equation. The difference between the equations considered in this paper and the previous one is that it makes…
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…
In this paper we develop a new approach to stochastic evolution equations with an unbounded drift $A$ which is dependent on time and the underlying probability space in an adapted way. It is well-known that the semigroup approach to…
This paper devotes to studying abstract stochastic evolution equations in M-type 2 Banach spaces. First, we handle nonlinear evolution equations with multiplicative noise. The existence and uniqueness of local and global mild solutions…
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…
A parameter estimation problem for a class of semilinear stochastic evolution equations is considered. Conditions for consistency and asymptotic normality are given in terms of growth and continuity properties of the nonlinear part.…
We study semi-linear evolutionary problems where the linear part is the generator of a positive $C_0$-semigroup. The non-linear part is assumed to be quasi-increasing. Given an initial value in between a sub- and a super-solution of the…
We study the asymptotic behavior of solutions to stochastic evolution equations with monotone drift and multiplicative Poisson noise in the variational setting, thus covering a large class of (fully) nonlinear partial differential equations…