The four papers in this volume examine attractors of partial differential equations, with a focus on investigation of elements of attractors. Unlike the finite-dimensional case of ordinary differential equations, an element of the attractor of a partial differential equation is itself a function of spatial variables. This dependence on spatial variables is investigated by asymptotic methods. For example, the asymptotics show that the turbulence generated in a tube by a large localized external force does not propagate to infinity along the tube if the flux of the flow is not too large. Another topic considered here is the dependence of attractors on singular perturbations of the equations. The theory of unbounded attractors of equations without bounded attracting sets is also covered. All of the articles are systematic and detailed, furnishing an excellent review of new approaches and techniques developed by the Moscow school.

Readership

Specialists in partial differential equations, dynamical systems, and mathematical physics.

Table of Contents

• A. V. Babin -- Asymptotic expansion at infinity of a strongly perturbed Poiseuille flow
• V. V. Chepyzhov and A. Yu. Goritskiĭ -- Unbounded attractors of evolution equations
• M. Yu. Skvortsov and M. I. Vishik -- Attractors of singularly perturbed parabolic equations, and asymptotic behavior of their elements
• V. Yu. Skvortsov and M. I. Vishik -- The asymptotics of solutions of reaction-diffusion equations with small parameter