相关论文: Perturbation of a nonautonomous problem in $\mathb…
In this paper we study the asymptotic behaviour of a nonlocal nonlinear parabolic equation governed by a parameter. After giving the existence of unique branch of solutions composed by stable solutions in stationary case, we gives for the…
We give both sufficient conditions and necessary conditions for the stochastic stability of non-uniformly expanding maps either with or without critical sets. We also show that the number of probability measures describing the statistical…
In this paper, the problem of partial stabilization of nonlinear systems along a given trajectory is considered. This problem is treated within the framework of stability of a family of sets. Sufficient conditions for the asymptotic…
It is shown that the emergence of obstacles to asymptotic integrability in the analysis of perturbed evolution equations may, often, be a consequence of the manner, in which the freedom in the ex-pansion is exploited in the derivation of…
This paper addresses the stability analysis of infinite-dimensional sampled-data systems under unbounded perturbations. We present two classes of unbounded perturbations preserving the exponential stability of sampled-data systems. To this…
In the present work we study the optimal control of an evolution equation with non-smooth dissipation. The solution mapping of this system is non-smooth and hence the analysis is quite challenging. Our approach is to regularize the…
We analyze the robustness of optimally controlled evolution equations with respect to spatially localized perturbations. We prove that if the involved operators are domain-uniformly stabilizable and detectable, then these localized…
In this work we study permanence of hyperbolicity for autonomous differential equations under nonautonomous random/stochastic perturbations. For the linear case, we study robustness and existence of exponential dichotomies for nonautonomous…
In this paper we study the asymptotic behaviour of a nonlocal nonlinear parabolic equation governed by a parameter. After giving the existence of unique branch of solutions composed by stable solutions in stationary case, we gives for the…
This thesis is concerned with the asymptotic behavior of solutions of stochastic $p$-Laplace equations driven by non-autonomous forcing on $\mathbb{R}^n$. Two cases are studied, with additive and multiplicative noise respectively. Estimates…
We consider abstract evolution equations with on-off time delay feedback. Without the time delay term, the model is described by an exponentially stable semigroup. We show that, under appropriate conditions involving the delay term, the…
We return to the subject of stability of infinite time asymptotics of kinetic equations. We found a model which is simpler than those studied previously and which shows unstable behavior corresponding to our arguments to appear elsewhere,…
This paper studies the asymptotic convergence properties of the primal-dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by…
In this work, we study the relations between bounded dynamic regret and the classical notion of asymptotic stability for the case of a priori unknown and time-varying cost functions. In particular, we show that bounded dynamic regret…
This paper considers the asymptotic behaviour of deterministically and stochastically forced linear pantograph equations. The asymptotic behaviour is studied in the case when all solutions of the pantograph equation without forcing tend to…
In this paper we study maximal $L^p$-regularity for evolution equations with time-dependent operators $A$. We merely assume a measurable dependence on time. In the first part of the paper we present a new sufficient condition for the…
This paper is devoted to the study of $L^p$-maximal regularity for non-autonomous linear evolution equations of the form \begin{equation*}\label{Multi-pert1-diss-non} \dot u(t)+A(t)B(t)u(t)=f(t)\ \ t\in[0,T],\ \ u(0)=u_0. \end{equation*}…
In this work, we study continuity and topological structural stability of attractors for nonautonomous random differential equations obtained by small bounded random perturbations of autonomous semilinear problems. First, we study existence…
This paper studies asymptotic behavior of solutions of a free boundary problem modeling the growth of tumors with two species of cells: proliferating cells and quiecent cells. In previous literatures it has been proved that this problem has…
In this paper, we study stability properties of nonuniform hyperbolicity for evolution processes associated with differential equations in Banach spaces. We prove a robustness result of nonuniform hyperbolicity for linear evolution…