This book develops the theory of global attractors for a class of parabolic PDEs that includes
reaction-diffusion equations and the Navier-Stokes equations, two examples that are treated …

In this paper, we study the long time behavior of a one-dimensional reaction diffusion system
appearing in mathematical biology by using the theory of infinite dimensional dynamical …

Nonlinear evolution equations arise in many fields of sciences including physics,
mechanics, and material science. This book introduces some important methods for dealing …

Dissipative equations have attracted substantial attention over many years. Much progress
has been achieved in this area using a combination of both finite dimensional and infinite …

We prove the existence of the universal attractor for the strongly damped semilinear wave
equation, in the presence of a quite general nonlinearity of critical growth. When the …

This monograph is devoted to the global existence, uniqueness and asymptotic behaviour of
smooth solutions to both initial value problems and initial boundary value problems for …

Finite dimensional exponential attractor for the phase field model Page 1 Applicnble Amlysis,
Vo1.49, pp. 197-212 Repnnts available directly from the publisher Photocopying permitted by …

Abstract CONTENTS Introduction § 1. Principal examples § 2. Global attractor. Existence
theorems § 3. Structure of a global attractor. Regularity conditions § 4. The finite …

The authors establish a global fast dynamics for a class of equations that include the beam
equations as studied by Ball (1973) and von Karman equations for a thin plate. They …

We construct the global bounded solutions and the attractors of a parabolic-parabolic
chemotaxis-growth system in two-and three-dimensional smooth bounded domains. We …