Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Attractors for Degenerate Parabolic Type Equations
 
Messoud Efendiev Hemholtz Center Munich, Neuherberg, Germany
Attractors for Degenerate Parabolic Type Equations
Hardcover ISBN:  978-1-4704-0985-2
Product Code:  SURV/192
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1084-1
Product Code:  SURV/192.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-1-4704-0985-2
eBook: ISBN:  978-1-4704-1084-1
Product Code:  SURV/192.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Attractors for Degenerate Parabolic Type Equations
Click above image for expanded view
Attractors for Degenerate Parabolic Type Equations
Messoud Efendiev Hemholtz Center Munich, Neuherberg, Germany
Hardcover ISBN:  978-1-4704-0985-2
Product Code:  SURV/192
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1084-1
Product Code:  SURV/192.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-1-4704-0985-2
eBook ISBN:  978-1-4704-1084-1
Product Code:  SURV/192.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 1922013; 221 pp
    MSC: Primary 35; 37;

    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 bounded domains, this attractor usually has finite Hausdorff and fractal dimension. 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 infinite fractal dimension.

    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 attractor of such degenerate equations that cannot be observed in the case of nondegenerate equations in bounded domains.

    This book is published in cooperation with Real Sociedád Matematica Española.
    Readership

    Graduate students and research mathematicians interested in non-linear PDEs.

  • Table of Contents
     
     
    • Chapters
    • 1. Auxiliary materials
    • 2. Global attractors for autonomous evolution equations
    • 3. Exponential attractors
    • 4. Porous medium equation in homogeneous media: Long-time dynamics
    • 5. Porous medium equation in heterogeneous media: Long-time dynamics
    • 6. Long-time dynamics of $p$-Laplacian equations: Homogeneous-media
    • 7. Long-time dynamics of $p$-Laplacian equations: Heterogeneous media
    • 8. Doubly nonlinear degenerate parabolic equations
    • 9. On a class of PDEs with degenerate diffusion and chemotaxis: Autonomous case
    • 10. On a class of PDEs with degenerate diffusion and chemotaxis: Nonautonomous case
    • 11. ODE-PDE coupling arising in the modelling of a forest ecosystem
  • Reviews
     
     
    • The main aim of this book is to give more insight into such types of PDEs and to fill this gap. This aim is achieved by a systematic study of the well-posedness and the dynamics of the associated semigroup generated by degenerate parabolic equations in terms of their global and exponential attractors as well as studying fractal dimension and Kolmogorov entropy.

      Zentralblatt Math
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1922013; 221 pp
MSC: Primary 35; 37;

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 bounded domains, this attractor usually has finite Hausdorff and fractal dimension. 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 infinite fractal dimension.

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 attractor of such degenerate equations that cannot be observed in the case of nondegenerate equations in bounded domains.

This book is published in cooperation with Real Sociedád Matematica Española.
Readership

Graduate students and research mathematicians interested in non-linear PDEs.

  • Chapters
  • 1. Auxiliary materials
  • 2. Global attractors for autonomous evolution equations
  • 3. Exponential attractors
  • 4. Porous medium equation in homogeneous media: Long-time dynamics
  • 5. Porous medium equation in heterogeneous media: Long-time dynamics
  • 6. Long-time dynamics of $p$-Laplacian equations: Homogeneous-media
  • 7. Long-time dynamics of $p$-Laplacian equations: Heterogeneous media
  • 8. Doubly nonlinear degenerate parabolic equations
  • 9. On a class of PDEs with degenerate diffusion and chemotaxis: Autonomous case
  • 10. On a class of PDEs with degenerate diffusion and chemotaxis: Nonautonomous case
  • 11. ODE-PDE coupling arising in the modelling of a forest ecosystem
  • The main aim of this book is to give more insight into such types of PDEs and to fill this gap. This aim is achieved by a systematic study of the well-posedness and the dynamics of the associated semigroup generated by degenerate parabolic equations in terms of their global and exponential attractors as well as studying fractal dimension and Kolmogorov entropy.

    Zentralblatt Math
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
You may be interested in...
Please select which format for which you are requesting permissions.