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Galerkin averaging method and Poincaré normal form for some quasilinear PDEs

Dario Bambusi (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We use the Galerkin averaging method to construct a coordinate transformation putting a nonlinear PDE in Poincaré normal form up to finite order. We also give a rigorous estimate of the remainder showing that it is small as a differential operator of very high order. The abstract theorem is then applied to a quasilinear wave equation, to the water wave problem and to a nonlinear heat equation. The normal form is then used to construct approximate solutions whose difference from true solutions is...

Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation

Nikolay Tzvetkov, Nicola Visciglia (2013)

Annales scientifiques de l'École Normale Supérieure

Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. The resulting measures are supported by Sobolev spaces of increasing regularity. We also prove a property on the support of these measures leading to the conjecture that they are indeed invariant by the flow of the Benjamin-Ono equation.

Generation of analytic semi-groups in L2 for a class of second order degenerate elliptic operators

Piermarco Cannarsa, Dario Rocchetti, Judith Vancostenoble (2008)

Control and Cybernetics

Global attraction to solitary waves in models based on the Klein-Gordon equation.

Komech, Alexander I., Komech, Andrew A. (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Global attractor for an equation modelling a thermostat.

de Cássia, Rita, Broche, D. S., de Oliveira, L. Augusto F., Pereira, Antônio L. (2003)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Global attractor for the generalized dissipative KdV equation with nonlinearity.

Zhang, Zai-Yun, Liu, Zhen-Hai (2011)

International Journal of Mathematics and Mathematical Sciences

Global attractor for the lattice dynamical system of a nonlinear Boussinesq equation.

Abdallah, Ahmed Y. (2005)

Abstract and Applied Analysis

Global attractors for a class of degenerate diffusion equations.

Takeuchi, Shingo, Yokota, Tomomi (2003)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Global attractors for problems with monotone operators

Alexandre N. Carvalho, Jan W. Cholewa, Tomasz Dlotko (1999)

Bollettino dell'Unione Matematica Italiana

L'esistenza di attrattori globali per equazioni paraboliche semilineari è stata estensivamente studiata da molti autori mentre il caso quasilineare è stato meno considerato e ancora esistono molti problemi aperti. L'obiettivo di questo lavoro è di studiare, da un punto di vista astratto, l'esistenza di attrattori globali per equazioni paraboliche quasilineari con parte principale monotona. I risultati ottenuti vengono applicati a problemi parabolici degeneri del secondo ordine e di ordine superiore....

Global dynamics of a reaction-diffusion system.

You, Yuncheng (2011)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Global existence of solutions to Schrödinger equations on compact riemannian manifolds below $H^{1}$

Sijia Zhong (2010)

Bulletin de la Société Mathématique de France

In this paper, we will study global well-posedness for the cubic defocusing nonlinear Schrödinger equations on the compact Riemannian manifold without boundary, below the energy space, i.e. $s < 1$ , under some bilinear Strichartz assumption. We will find some $\tilde{s} < 1$ , such that the solution is global for $s > \tilde{s}$ .

Global stability of travelling fronts for a damped wave equation with bistable nonlinearity

Thierry Gallay, Romain Joly (2009)

Annales scientifiques de l'École Normale Supérieure

We consider the damped wave equation $α u_{t t} + u_{t} = u_{x x} - V^{'} (u)$ on the whole real line, where $V$ is a bistable potential. This equation has travelling front solutions of the form $u (x, t) = h (x - s t)$ which describe a moving interface between two different steady states of the system, one of which being the global minimum of $V$ . We show that, if the initial data are sufficiently close to the profile of a front for large $| x |$ , the solution of the damped wave equation converges uniformly on $ℝ$ to a travelling front as $t \to + \infty$ . The proof of this global stability...

Gradient systems of closed operators

Vittorino Pata (2009)

Open Mathematics

A classical result on the existence of global attractors for gradient systems is extended to the case of a semigroup S(t) lacking strong continuity, but satisfying the weaker property of being a closed map for every fixed t ≥ 0.

Group actions on monotone skew-product semiflows with applications

Feng Cao, Mats Gyllenberg, Yi Wang (2016)

Journal of the European Mathematical Society

We discuss a general framework of monotone skew-product semiflows under a connected group action. In a prior work, a compact connected group $G$ -action has been considered on a strongly monotone skew-product semiflow. Here we relax the strong monotonicity and compactness requirements, and establish a theory concerning symmetry or monotonicity properties of uniformly stable 1-cover minimal sets. We then apply this theory to show rotational symmetry of certain stable entire solutions for a class of...

Currently displaying 1 – 14 of 14

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