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The Resource Attractors for degenerate parabolic type equations, Messoud Efendiev

Attractors for degenerate parabolic type equations, Messoud Efendiev

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Creator

Efendiev, Messoud

Author

Efendiev, Messoud

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

Language: eng

Work

Publication

Providence, Rhode Island, American Mathematical Society, Madrid, Spain, Real Sociedad Mathematica Espanola, 2013

Extent: x, 221 pages

Isbn: 9781470409852

Instance

Label: Attractors for degenerate parabolic type equations

Title: Attractors for degenerate parabolic type equations

Statement of responsibility: Messoud Efendiev

Creator

Efendiev, Messoud

Author

Efendiev, Messoud

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

Mathematical surveys and monographs, no. 192

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