Related papers: Continuity and averaging for parabolic evolution s…
We investigate an abstract wave equation with a time-dependent propagation speed, and we consider both the non-dissipative case, and the case with a strong damping that depends on a power of the elastic operator. Previous results show that,…
We develop a new tool, the time inhomogeneous Poisson equation in the whole space and with a terminal condition at infinity, to study the asymptotic behavior of the non-autonomous multi-scale stochastic system with irregular coefficients,…
We consider a family of second-order parabolic operators $\partial_t+\mathcal{L}_\varepsilon$ in divergence form with rapidly oscillating, time-dependent and almost-periodic coefficients. We establish uniform interior and boundary H\"older…
The paper presents necessary and sufficient conditions for a nonlinear system to be stabilized by a feedback. The conditions are based on the ideas related to the well-known Pontryagin's maximum principle. That allows us to formulate the…
We present a general method for studying long time asymptotics of nonlinear parabolic partial differential equations. The method does not rely on a priori estimates such as the maximum principle. It applies to systems of coupled equations,…
A wide class of non-autonomous nonlinear parabolic partial differential equations with delay is studied. We allow in our investigations different types of delays such as constant, time-dependent, state-dependent (both discrete and…
We apply functional analytical and variational methods in order to study well-posedness and qualitative properties of evolution equations on product Hilbert spaces. To this aim we introduce an algebraic formalism for matrices of…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
A study of time homogeneous, real valued Markov processes with a special property and a non-atomic initial distribution is provided. The new notion of a function of evolution of distribution which determines the dependency between one…
We introduce a new machinery to study the large time behavior for general classes of Hamilton--Jacobi type equations, which include degenerate parabolic equations and weakly coupled systems. We establish the convergence results by using the…
An autonomous system of ordinary differential equations describing nonlinear oscillations on the plane is considered. The influence of time-dependent perturbations decaying at infinity in time is investigated. It is assumed that the…
We prove the averaging principle for a class of stochastic systems. The slow component is solution to a fractional differential equation, which is coupled with a fast component considered as solution to an ergodic stochastic differential…
While the asymptotic stability of positive linear systems in the presence of bounded time delays has been thoroughly investigated, the theory for nonlinear positive systems is considerably less well-developed. This paper presents a set of…
We prove a new linearization principle for the nonlinear stability of solutions to semilinear evolution equations of parabolic type. We assume that the set of equilibria forms a finite dimensional manifold of normally stable and normally…
The averaging method provides a powerful tool for studying evolution in near-integrable systems. Existence of separatrices in the phase space of the underlying integrable system is an obstacle for application of standard results that…
In theoretical ecology, models describing the spatial dispersal and the temporal evolution of species having non-overlapping generations are often based on integrodifference equations. For various such applications the environment has an…
We establish the local H\"older continuity for the nonnegative weak solutions of certain doubly nonlinear parabolic equations possessing a singularity in the time derivative part and a degeneracy in the principal part. The proof involves…
Using Zvonkin's transform and the Poisson equation in $R^d$ with a parameter, we prove the averaging principle for stochastic differential equations with time-dependent H\"older continuous coefficients. Sharp convergence rates with order…
We consider the non-degenerate second-order parabolic partial differential equations of non-divergence form with bounded measurable coefficients (not necessary continuous). Under some assumptions it is known that the fundamental solution to…
We consider linear inhomogeneous non-autonomous parabolic problems associated to sesquilinear forms, with discontinuous dependence of time. We show that for these problems, the property of maximal parabolic regularity can be extrapolated to…