相关论文: Asymptotic Behavior of Solutions of Complex Discre…
We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the…
Blowup analysis for solutions of a general evolution equation with nonlocal diffusion and localized source is performed. By comparison with recent results on global-in-time solutions, a dichotomy result is obtained.
The Lindblad equation describes the dissipative time evolution of a density matrix that characterizes an open quantum system in contact with its environment. The widespread ensemble interpretation of a density matrix requires its time…
We consider two types of the time-dependent Ginzburg-Landau equation in 2D bounded domains: the heat-flow equation and the Schroedinger equation. The system of ordinary differential equations is obtained that describes the evolution of the…
The aim of this paper is to apply the modified potential well method and some new differential inequalities to study the asymptotic behavior of solutions to the initial homogeneous $\hbox{Neumann}$ problem of a nonlinear diffusion equation…
We study the Cauchy problem for the focusing nonlinear Kundu-Eckhaus equation and construct long time asymptotic expansion of its solution in fixed space-time cone with $C(x_1,x_2,v_1,v_2)=\{(x,t)\in\Re^2:x=x_0+vt$…
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 prove the asymptotic stability of the moving kinks for the nonlinear relativistic wave equations in one space dimension with a Ginzburg-Landau potential: starting in a small neighborhood of the kink, the solution, asymptotically in time,…
This paper deals with nonlinear parabolic equation for which a local solution in time exists and then blows up in a finite time. We consider the Chipot-Weissler equation. We study the numerical approximation, we show that the numerical…
We study the asymptotic behavior and the scattering from infinity problem for the massive Maxwell-Klein-Gordon system in the Lorenz gauge, which were previously only studied for the massless system. For a general class of initial data, in…
We study the asymptotic behavior of solutions of discrete nonlinear Schr\"odinger-type (DNLS) equations. For a conservative system, we consider the global in time solvability and the question of existence of standing wave solutions.…
The asymptotic behavior of a nonlinear diffusive equation obtained in the framework of the $\kappa$-generalized statistical mechanics is studied. The analysis based on the classical Lie symmetry shows that the $\kappa$-Gaussian function is…
In this paper, we mainly discuss asymptotic profiles of solutions to a class of abstract second-order evolution equations of the form $u''+Au+u'=0$ in real Hilbert spaces, where $A$ is a nonnegative selfadjoint operator. The main result is…
We study the large time behavior of solutions to a non-local diffusion equation, $u_t=J*u-u$ with $J$ smooth, radially symmetric and compactly supported, posed in $\mathbb{R}_+$ with zero Dirichlet boundary conditions. In sets of the form…
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…
Using some classical methods of dynamical systems, stability results and asymptotic decay of strong solutions for the complex Ginzburg-Landau equation (CGL), $$ \partial_t u = (a + i\alpha) \Delta u - (b + i \beta) |u|^\sigma u + k u, \,\,…
We report the existence of stable symmetric vortex-type solutions for two-dimensional nonlinear discrete dissipative systems governed by a cubic-quintic complex Ginzburg-Landau equation. We construct a whole family of vortex solitons with a…
We consider the large time asymptotic behavior of the global solutions to the initial value problem for the nonlinear damped wave equation with slowly decaying initial data. When the initial data decay fast enough, it is known that the…
In this article we study the long-time behavior of incompressible ideal flow in a half plane from the point of view of vortex scattering. Our main result is that certain asymptotic states for half-plane vortex dynamics decompose naturally…
In this paper, we consider the complex Ginzburg--Landau equation $u_t = e^{i\theta} [\Delta u + |u|^\alpha u] + \gamma u$ on ${\mathbb R}^N $, where $\alpha >0$, $\gamma \in \R$ and $-\pi /2<\theta <\pi /2$. By convexity arguments we prove…