Attractors for degenerate parabolic type equations

Resource Information

The work Attractors for degenerate parabolic type equations represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.

Label

Attractors for degenerate parabolic type equations

Statement of responsibility

Messoud Efendiev

Creator

• Efendiev, Messoud

Author

• Efendiev, Messoud

Subject

• Dynamical systems and ergodic theory -- Infinite-dimensional dissipative dynamical systems -- Attractors and their dimensions, Lyapunov exponents
• Dynamical systems and ergodic theory -- Infinite-dimensional dissipative dynamical systems -- General theory, nonlinear semigroups, evolution equations
• Partial differential equations -- Parabolic equations and systems -- Degenerate parabolic equations
• Partial differential equations -- Parabolic equations and systems -- Nonlinear parabolic equations
• Partial differential equations -- Parabolic equations and systems -- Quasilinear parabolic equations
• Degenerate differential equations
• Differential equations, Parabolic

Language

eng

Summary

This book deals with the long-time behavior of solutions of degenerate parabolic dissipative equations arising in the study of biological, ecological, and physical problems. Examples include porous media equations, p-Laplacian and doubly nonlinear equations, as well as degenerate diffusion equations with chemotaxis and ODE-PDE coupling systems. For the first time, the long-time dynamics of various classes of degenerate parabolic equations, both semilinear and quasilinear, are systematically studied in terms of their global and exponential attractors. The long-time behavior of many dissipative systems generated by evolution equations of mathematical physics can be described in terms of global attractors. In the case of dissipative PDEs in bonded domains, this attractor usually has finite Hausdorff and fractal dimention. Hence, if the global attractor exists, its defining property guarantees that the dynamical system reduced to the attractor contains all of the nontrivial dynamics of the original system. Moreover, the reduced phase space is really "thinner" than the initial phase space. However, in contrast to nondegenerate parabolic type equations, for a quite large class of degenerate parabolic type equations, their global attractors can have infinate fractal dimention. The main goal of the present book is to give a detailed and systematic study of the well-posedness and the dynamics of the semigroup associated to important degenerate parabolic equations in terms of their global and exponential attractors. Fundamental topics include existence of attractors, convergence of the dynamics and the rate of convergence, as well as the determination of the fractal dimension and the Kolmogorov entropy of corresponding attractors. The analysis and results in this book show that there are new effects related to the attractors of such degenerate equations that cannot be observed in the case of nondegenerate equations in bounded domains

Member of

• Mathematical surveys and monographs, no. 192

Cataloging source

DLC

Dewey number

515/.3534

Index

index present

LC call number

QA377

LC item number

.E37 2013

Literary form

non fiction

Nature of contents

bibliography

Series statement

Mathematical surveys and monographs

Series volume

volume 192