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Asymptotics for some nonlinear damped wave equation : finite time convergence versus exponential decay results

B. Baji, A. Cabot, J. I. Díaz (2007)

Annales de l'I.H.P. Analyse non linéaire

Asymptotics for the minimization of a Ginzburg-Landau energy in n dimensions

Paweł Strzelecki (1996)

Colloquium Mathematicae

We prove that minimizers $u \in W^{1, n}$ of the functional $E_{} (u) = 1 / n \int_{|} {\nabla u |}^{n} d x + 1 / (4^{n}) \int_{(} 1 - {| u |}^{2})^{2} d x$ , ⊂ $ℝ^{n}$ , n ≥ 3, which satisfy the Dirichlet boundary condition $u_{} = g$ on for g: → $S^{n - 1}$ with zero topological degree, converge in $W^{1, n}$ and $C_{l o c}^{α}$ for any α<1 - upon passing to a subsequence $_{k} \to 0$ - 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 $□ u = m^{2} u + G (t, x, u, u_{x}, u_{t}),$ , II. Scattering theory

John M. Chadam (1972)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Asymptotics for $□ u = m^{2} u + G (x, t, u, u_{x}, u_{t}),$ I. Global existence and decay

John M. Chadam (1972)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Asymptotics of parabolic equations with possible blow-up

Radosław Czaja (2004)

Colloquium Mathematicae

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 sums of subcoercive operators

Nick Dungey, A. ter Elst, Derek Robinson (1999)

Colloquium Mathematicae

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...