Coverart for item
The Resource Attractors for degenerate parabolic type equations, Messoud Efendiev

Attractors for degenerate parabolic type equations, Messoud Efendiev

Label
Attractors for degenerate parabolic type equations
Title
Attractors for degenerate parabolic type equations
Statement of responsibility
Messoud Efendiev
Creator
Author
Subject
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
Cataloging source
DLC
http://library.link/vocab/creatorName
Efendiev, Messoud
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
http://library.link/vocab/subjectName
  • Differential equations, Parabolic
  • Degenerate differential equations
  • Partial differential equations -- Parabolic equations and systems -- Nonlinear parabolic equations
  • Partial differential equations -- Parabolic equations and systems -- Quasilinear parabolic equations
  • Partial differential equations -- Parabolic equations and systems -- Degenerate parabolic equations
  • Dynamical systems and ergodic theory -- Infinite-dimensional dissipative dynamical systems -- General theory, nonlinear semigroups, evolution equations
  • Dynamical systems and ergodic theory -- Infinite-dimensional dissipative dynamical systems -- Attractors and their dimensions, Lyapunov exponents
Label
Attractors for degenerate parabolic type equations, Messoud Efendiev
Instantiates
Publication
Copyright
Bibliography note
Includes bibliographical references and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier.
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Control code
848267256
Dimensions
26 cm
Extent
x, 221 pages
Isbn
9781470409852
Isbn Type
(alk. paper)
Lccn
2013016419
Media category
unmediated
Media MARC source
rdamedia.
Media type code
  • n
System control number
(OCoLC)848267256
Label
Attractors for degenerate parabolic type equations, Messoud Efendiev
Publication
Copyright
Bibliography note
Includes bibliographical references and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier.
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Control code
848267256
Dimensions
26 cm
Extent
x, 221 pages
Isbn
9781470409852
Isbn Type
(alk. paper)
Lccn
2013016419
Media category
unmediated
Media MARC source
rdamedia.
Media type code
  • n
System control number
(OCoLC)848267256

Library Locations

    • Mathematical Sciences LibraryBorrow it
      104 Ellis Library, Columbia, MO, 65201, US
      38.944377 -92.326537
Processing Feedback ...