相关论文: On convergence towards a self-similar solution for…
We discuss an eigenvalue problem which arises in the studies of asymptotic stability of a self-similar attractor in the sigma model. This problem is rather unusual from the viewpoint of the spectral theory of linear operators and requires…
We exhibit a singularly perturbed parabolic problems for which the asymptotic behavior can be described by an one-dimensional ordinary differential equation. We estimate the continuity of attractors in the Hausdorff metric by rate of…
In this paper, several results concerning attraction and asymptotic stability in the large of nonlinear ordinary differential equations are presented. The main result is very simple to apply yielding a sufficient condition under which the…
In this article, we prove the exponential stabilization of the semilinear wave equation with a damping effective in a zone satisfying the geometric control condition only. The nonlinearity is assumed to be subcritical, defocusing and…
The wave equation with energy critical sources and nonlinear damping defined on a 3D bounded domain is considered. It is shown that the resulting dynamical system admits a global attractor. Under the additional assumption of strong…
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…
In this paper we study the asymptotic nonlinear dynamics of scalar semilinear parabolic problems reaction-diffusion type when the diffusion coefficient becomes large in a subregion which is interior to the domain. We obtain, under suitable…
We study the global well-posedness and asymptotic behavior for a semilinear damped wave equation with Neumann boundary conditions, modelling a one-dimensional linearly elastic body interacting with a rigid substrate through an adhesive…
We study asymptotic stability of solitary wave solutions in the one-dimensional Benney-Luke equation, a formally valid approximation for describing two-way water wave propagation. For this equation, as for the full water wave problem, the…
We consider the Cauchy problem for an energy supercritical nonlinear wave equation that arises in $(1+5)$--dimensional Yang--Mills theory. A certain self--similar solution $W_0$ of this model is conjectured to act as an attractor for…
We establish asymptotic gain along with input-to-state practical stability results for disturbed semilinear systems w.r.t. the global attractor of the respective undisturbed system. We apply our results to a large class of nonlinear…
We exhibit a class of singularly perturbed parabolic problems which the asymptotic behavior can be described by a system of ordinary differential equation. We estimate the convergence of attractors in the Hausdorff metric by rate of…
We are concerned with the dynamical behavior of solutions to semilinear wave systems with time-varying damping and nonconvex force potential. Our result shows that the dynamical behavior of solution is asymptotically stable without any…
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and…
We apply the dynamical approach to the study of the second order semi-linear elliptic boundary value problem in a cylindrical domain with a small parameter at the second derivative with respect to the "time" variable corresponding to the…
We prove nonlinear stability of the fundamental self--similar solution of the wave equation with a focusing power nonlinearity $\psi_{tt}-\Delta \psi=\psi^p$ for $p=3,5,7,...$ in the radial case. The proof is based on a semigroup…
We study the non-autonomous weakly damped wave equation with subquintic growth condition on the nonlinearity. Our main focus is the class of Shatah--Struwe solutions, which satisfy the Strichartz estimates and are coincide with the class of…
In this paper, we study transverse linear stability of line solitary waves to the $2$-dimensional Benney-Luke equation which arises in the study of small amplitude long water waves in $3$D. In the case where the surface tension is weak or…
We consider the one-dimensional nonlinear Schr\"odinger equation with an attractive delta potential and mass-supercritical nonlinearity. This equation admits a one-parameter family of solitary wave solutions in both the focusing and…
We investigate the stability of the wave equation with spatial dependent coefficients on a bounded multidimensional domain. The system is stabilized via a scattering passive feedback law. We formulate the wave equation in a port-Hamiltonian…