Degenerate 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 Degenerate Parabolic Equations write by Emmanuele DiBenedetto. This book was released on 2012-12-06. Degenerate Parabolic Equations available in PDF, EPUB and Kindle. Evolved from the author's lectures at the University of Bonn's Institut für angewandte Mathematik, this book reviews recent progress toward understanding of the local structure of solutions of degenerate and singular parabolic partial differential equations.
Harnack's Inequality for Degenerate and Singular Parabolic Equations
Harnack's Inequality for Degenerate and Singular 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 Harnack's Inequality for Degenerate and Singular Parabolic Equations write by Emmanuele DiBenedetto. This book was released on 2011-11-13. Harnack's Inequality for Degenerate and Singular Parabolic Equations available in PDF, EPUB and Kindle. Degenerate and singular parabolic equations have been the subject of extensive research for the last 25 years. Despite important achievements, the issue of the Harnack inequality for non-negative solutions to these equations, both of p-Laplacian and porous medium type, while raised by several authors, has remained basically open. Recently considerable progress has been made on this issue, to the point that, except for the singular sub-critical range, both for the p-laplacian and the porous medium equations, the theory is reasonably complete. It seemed therefore timely to trace a comprehensive overview, that would highlight the main issues and also the problems that still remain open. The authors give a comprehensive treatment of the Harnack inequality for non-negative solutions to p-laplace and porous medium type equations, both in the degenerate (p/i”2 or im/i”1) and in the singular range (1“ip/i2 or 0“im/i
Degenerate Nonlinear Diffusion Equations
Degenerate Nonlinear Diffusion 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 Degenerate Nonlinear Diffusion Equations write by Angelo Favini. This book was released on 2012-05-08. Degenerate Nonlinear Diffusion Equations available in PDF, EPUB and Kindle. The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asymptotic behaviour, discretization schemes, coefficient identification, and to introduce relevant solving methods for each of them.
Attractors for Degenerate Parabolic Type Equations
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).
Degenerate Differential Equations in Banach Spaces
Degenerate Differential Equations in Banach Spaces - 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 Degenerate Differential Equations in Banach Spaces write by Angelo Favini. This book was released on 1998-09-10. Degenerate Differential Equations in Banach Spaces available in PDF, EPUB and Kindle. This work presents a detailed study of linear abstract degenerate differential equations, using both the semigroups generated by multivalued (linear) operators and extensions of the operational method from Da Prato and Grisvard. The authors describe the recent and original results on PDEs and algebraic-differential equations, and establishes the analyzability of the semigroup generated by some degenerate parabolic operators in spaces of continuous functions.
