Asymptotics for some nonlinear damped wave equation : finite time convergence versus exponential decay results
Asymptotics for the minimization of a Ginzburg-Landau energy in n dimensions
We prove that minimizers of the functional , ⊂ , n ≥ 3, which satisfy the Dirichlet boundary condition on for g: → with zero topological degree, converge in and for any α<1 - upon passing to a subsequence - to some minimizing n-harmonic map. This is a generalization of an earlier result obtained for n=2 by Bethuel, Brezis, and Hélein. An example of nonunique asymptotic behaviour (which cannot occur in two dimensions if deg g = 0) is presented.
Asymptotics for , II. Scattering theory
Asymptotics for I. Global existence and decay
Asymptotics of parabolic equations with possible blow-up
We describe the long-time behaviour of solutions of parabolic equations in the case when some solutions may blow up in a finite or infinite time. This is done by providing a maximal compact invariant set attracting any initial data for which the corresponding solution does not blow up. The abstract result is applied to the Frank-Kamenetskii equation and the N-dimensional Navier-Stokes system with small external force.
Asymptotics of solutions to the Dirichlet-Cauchy problem for parabolic equations in domains with edges
This paper is concerned with the Dirichlet-Cauchy problem for second order parabolic equations in domains with edges. The asymptotic behaviour of the solution near the edge is studied.
Asymptotics of sums of subcoercive operators
We examine the asymptotic, or large-time, behaviour of the semigroup kernel associated with a finite sum of homogeneous subcoercive operators acting on a connected Lie group of polynomial growth. If the group is nilpotent we prove that the kernel is bounded by a convolution of two Gaussians whose orders correspond to the highest and lowest orders of the homogeneous subcoercive components of the generator. Moreover we establish precise asymptotic estimates on the difference of the kernel and the...
Asymptotics of the first boundary problem for elliptic equations in a domain with thin covering.
Asymptotics of the first nodal line
Asymptotics of the Nodal Lines of Solutions of 2-Dimensional Schrödinger Equations.
Asymptotics of time harmonic solutions to a thin ferroelectric model.
Asypmtotic Behaviour in Lr for Weak Solutions of the Navier-Stokes Equations in Exterior Domains.
Attracteurs compacts pour des problèmes d'évolution sans unicité
Attractivity of nonlinear impulsive delay differential equations.
Attractor for a viscous coupled Camassa-Holm equation.
Attractor of a semi-discrete Benjamin-Bona-Mahony equation on ℝ¹
This paper is concerned with the study of the large time behavior and especially the regularity of the global attractor for the semi-discrete in time Crank-Nicolson scheme to discretize the Benjamin-Bona-Mahony equation on ℝ¹. Firstly, we prove that this semi-discrete equation provides a discrete infinite-dimensional dynamical system in H¹(ℝ¹). Then we prove that this system possesses a global attractor in H¹(ℝ¹). In addition, we show that the global attractor is regular, i.e., is actually...
Attractors for a class of doubly nonlinear parabolic systems.
Attractors for general operators
In this article we introduce the notion of a minimal attractor for families of operators that do not necessarily form semigroups. We then obtain some results on the existence of the minimal attractor. We also consider the nonautonomous case. As an application, we obtain the existence of the minimal attractor for models of Cahn-Hilliard equations in deformable elastic continua.
Attractors for stochastic reaction-diffusion equation with additive homogeneous noise
We study the asymptotic behaviour of solutions of a reaction-diffusion equation in the whole space driven by a spatially homogeneous Wiener process with finite spectral measure. The existence of a random attractor is established for initial data in suitable weighted -space in any dimension, which complements the result from P. W. Bates, K. Lu, and B. Wang (2013). Asymptotic compactness is obtained using elements of the method of short trajectories.
Attractors of a Schrödinger-Poisson system