Attractors for Degenerate Parabolic Type Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Attractors for Degenerate Parabolic Type Equations write by Messoud Efendiev. This book was released on 2013-09-26. Attractors for Degenerate Parabolic Type Equations available in PDF, EPUB and Kindle. 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, -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 Sociedad Matemática Española (RSME).
Strange Attractors for Periodically Forced Parabolic Equations
Strange Attractors for Periodically Forced Parabolic Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Strange Attractors for Periodically Forced Parabolic Equations write by Kening Lu. This book was released on 2013. Strange Attractors for Periodically Forced Parabolic Equations available in PDF, EPUB and Kindle. "We prove that in systems undergoing Hopf bifurcations, the effects of periodic forcing can be amplified by the shearing in the system to create sustained chaotic behavior. Specifically, strange attractors with SRB measures are shown to exist. The analysis is carried out for infinite dimensional systems, and the results are applicable to partial differential equations. Application of the general results to a concrete equation, namely the Brusselator, is given."--Page v.
Recent Trends in Dynamical Systems
Recent Trends in Dynamical Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Recent Trends in Dynamical Systems write by Andreas Johann. This book was released on 2013-09-24. Recent Trends in Dynamical Systems available in PDF, EPUB and Kindle. This book presents the proceedings of a conference on dynamical systems held in honor of Jürgen Scheurle in January 2012. Through both original research papers and survey articles leading experts in the field offer overviews of the current state of the theory and its applications to mechanics and physics. In particular, the following aspects of the theory of dynamical systems are covered: - Stability and bifurcation - Geometric mechanics and control theory - Invariant manifolds, attractors and chaos - Fluid mechanics and elasticity - Perturbations and multiscale problems - Hamiltonian dynamics and KAM theory Researchers and graduate students in dynamical systems and related fields, including engineering, will benefit from the articles presented in this volume.
Global Attractors in Abstract Parabolic Problems
Global Attractors in Abstract Parabolic Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Global Attractors in Abstract Parabolic Problems write by Jan W. Cholewa. This book was released on 2000-08-31. Global Attractors in Abstract Parabolic Problems available in PDF, EPUB and Kindle. This book investigates the asymptotic behaviour of dynamical systems corresponding to parabolic equations.
Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations
Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations write by Messoud Efendiev. This book was released on 2018-10-17. Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations available in PDF, EPUB and Kindle. This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as finite dimensional reduction of their dynamics requires new ideas and tools. To this end, both a trajectory dynamical systems approach and new Liouville type results for the solutions of some class of elliptic equations are used. The work also uses symmetry and monotonicity results for nonnegative solutions in order to characterize an asymptotic profile of solutions and compares a pure elliptic partial differential equations approach and a dynamical systems approach. The new results obtained will be particularly useful for mathematical biologists.
