Related papers: A non-autonomous bifurcation problem for a non-loc…

In this paper we investigate a class of nonautonomous linear parabolic problems with time depending Ornstein-Uhlenbeck operators. We study the asymptotic behavior of the associated evolution operator and evolution semigroup in the periodic…

We consider the Cauchy problem for doubly nonlinear degenerate parabolic equations with inhomogeneous density on noncompact Riemannian manifolds. We give a qualitative classification of the behavior of the solutions of the problem depending…

We study the asymptotic behavior of solutions for the semilinear damped wave equation with variable coefficients. We prove that if the damping is effective, and the nonlinearity and other lower order terms can be regarded as perturbations,…

We consider the asymptotic behavior of solutions of the difference equations of the form $x(n+1)=Ax(n) + \sum_{k=0}^n B(n-k)x(k) + y(n)$ in a Banach space $\X$, where $n=0,1,2,...$; $A,B(n)$ are linear bounded operator in $\X$. Our method…

In some cases, solutions to nonlinear PDEs happen to be asymptotically (for large $x$ and/or $t$) invariant under a group $G$ which is not a symmetry of the equation. After recalling the geometrical meaning of symmetries of differential…

Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are…

The paper is devoted to the study of asymptotic behavior of solutions for nonlocal elliptic problems in weighted spaces. We deal with the most difficult case where the support of nonlocal terms intersects with the boundary of a plane…

The aim of this paper is to provide a comprehensive study of some linear nonlocal diffusion problems in metric measure spaces. These include, for example, open subsets in $\mathbb{R}^N$, graphs, manifolds, multi-structures or some fractal…

We study the behaviour of solutions of linear non-autonomous parabolic equations subject to Dirichlet or Neumann boundary conditions under perturbation of the domain. We prove that Mosco convergence of function spaces for non-autonomous…

In this paper we establish asymptotic (biasymptotic) equivalence between spaces of solutions of a given linear homogeneous system and a perturbed system. The perturbations are of either linear or weakly linear characters. Existence of a…

In this paper we study the asymptotic behavior of solutions of fractional differential equations of the form $ D^{\alpha}_Cu(t)=Au(t)+f(t), u(0)=x, 0<\alpha\le1, ( *) $ where $D^{\alpha}_Cu(t)$ is the derivative of the function $u$ in the…

We study a nonlinear pseudodifferential equation describing the dynamics of dislocations. The long time asymptotics of solutions is described by the self-similar profiles.

A mathematical model describing the capture of nonlinear systems into the autoresonance by a combined parametric and external periodic slowly varying perturbation is considered. The autoresonance phenomenon is associated with solutions…

We consider the slow nonlinear diffusion equation subject to a constant absorption rate and construct local self-similar solutions for reversing (and anti-reversing) interfaces, where an initially advancing (receding) interface gives way to…

We study an asymptotic behavior of solutions to elliptic equations of the second order in a two dimensional exterior domain. Under the assumption that the solution belongs to $L^q$ with $q \in [2,\infty)$, we prove a pointwise asymptotic…

This paper is devoted to studying non-commensurate fractional order planar systems. Our contributions are to derive sufficient conditions for the global attractivity of non-trivial solutions to fractional-order inhomogeneous linear planar…

In this paper, we consider the large time asymptotic behavior of solutions to systems of two cubic nonlinear Klein-Gordon equations in one space dimension. We classify the systems by studying the quotient set of a suitable subset of systems…

We consider an abstract first order evolution equation in a Hilbert space in which the linear part is represented by a self-adjoint nonnegative operator A with discrete spectrum, and the nonlinear term has order greater than one at the…

This paper investigates the asymptotic behaviors of global solutions to fourth-order parabolic and hyperbolic equations with Dirichlet boundary conditions. The equations model Micro-Electro-Mechanical Systems (MEMS) and are depending on a…

We consider a time-dependent linear diffusion equation together with a related inverse boundary value problem. The aim of the inverse problem is to determine, based on observations on the boundary, the non-homogeneous diffusion coefficient…