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Comparison Principles For Fully Nonlinear Parabolic Equations And Regularity Theory For Weak Solutions Of Parabolic Systems In Carnot Groups
Download Comparison Principles For Fully Nonlinear Parabolic Equations And Regularity Theory For Weak Solutions Of Parabolic Systems In Carnot Groups full books in PDF, epub, and Kindle. Read online Comparison Principles For Fully Nonlinear Parabolic Equations And Regularity Theory For Weak Solutions Of Parabolic Systems In Carnot Groups ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Book Synopsis Comparison Principles for Fully-nonlinear Parabolic Equations and Regularity Theory for Weak Solutions of Parabolic Systems in Carnot Groups by : Erin Rachel Haller
Download or read book Comparison Principles for Fully-nonlinear Parabolic Equations and Regularity Theory for Weak Solutions of Parabolic Systems in Carnot Groups written by Erin Rachel Haller and published by . This book was released on 2008 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dissertation Abstracts International by :
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2008 with total page 886 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the partial regularity of weak solutions of nonlinear parabolic systems by : Mariano Giaquinta
Download or read book On the partial regularity of weak solutions of nonlinear parabolic systems written by Mariano Giaquinta and published by . This book was released on 1981 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Strongly Coupled Parabolic and Elliptic Systems by : Dung Le
Download or read book Strongly Coupled Parabolic and Elliptic Systems written by Dung Le and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-05 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Strongly coupled (or cross-diffusion) systems of parabolic and elliptic partial differential equations appear in many physical applications. This book presents a new approach to the solvability of general strongly coupled systems, a much more difficult problem in contrast to the scalar case, by unifying, elucidating and extending breakthrough results obtained by the author, and providing solutions to many open fundamental questions in the theory. Several examples in mathematical biology and ecology are also included. Contents Interpolation Gagliardo–Nirenberg inequalities The parabolic systems The elliptic systems Cross-diffusion systems of porous media type Nontrivial steady-state solutions The duality RBMO(μ)–H1(μ)| Some algebraic inequalities Partial regularity
Book Synopsis Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications by : Victor A. Galaktionov
Download or read book Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications written by Victor A. Galaktionov and published by CRC Press. This book was released on 2004-05-24 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike the classical Sturm theorems on the zeros of solutions of second-order ODEs, Sturm's evolution zero set analysis for parabolic PDEs did not attract much attention in the 19th century, and, in fact, it was lost or forgotten for almost a century. Briefly revived by Pólya in the 1930's and rediscovered in part several times since, it was not until the 1980's that the Sturmian argument for PDEs began to penetrate into the theory of parabolic equations and was found to have several fundamental applications. Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications focuses on geometric aspects of the intersection comparison for nonlinear models creating finite-time singularities. After introducing the original Sturm zero set results for linear parabolic equations and the basic concepts of geometric analysis, the author presents the main concepts and regularity results of the geometric intersection theory (G-theory). Here he considers the general singular equation and presents the geometric notions related to the regularity and interface propagation of solutions. In the general setting, the author describes the main aspects of the ODE-PDE duality, proves existence and nonexistence theorems, establishes uniqueness and optimal Bernstein-type estimates, and derives interface equations, including higher-order equations. The final two chapters explore some special aspects of discontinuous and continuous limit semigroups generated by singular parabolic equations. Much of the information presented here has never before been published in book form. Readable and self-contained, this book forms a unique and outstanding reference on second-order parabolic PDEs used as models for a wide range of physical problems.
Book Synopsis On The Regularity Theory Of Fully Nonlinear Parabolic Equations by : Lihe Wang
Download or read book On The Regularity Theory Of Fully Nonlinear Parabolic Equations written by Lihe Wang and published by . This book was released on 1988 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Control of Nonlinear Parabolic Systems by : Pekka Neittaanmaki
Download or read book Optimal Control of Nonlinear Parabolic Systems written by Pekka Neittaanmaki and published by CRC Press. This book was released on 1994-02-08 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses theoretical approaches to the study of optimal control problems governed by non-linear evolutions - including semi-linear equations, variational inequalities and systems with phase transitions. It also provides algorithms for solving non-linear parabolic systems and multiphase Stefan-like systems.
Book Synopsis Qualitative Theory of Parabolic Equations, Part 1 by : T. I. Zelenyak
Download or read book Qualitative Theory of Parabolic Equations, Part 1 written by T. I. Zelenyak and published by Walter de Gruyter. This book was released on 2011-09-06 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the qualitative theory of ordinary differential equations, the Liapunov method plays a fundamental role. To use their analogs for the analysis of stability of solutions to parabolic, hyperparabolic, and other nonclassical equations and systems, time-invariant a priori estimates have to be devised for solutions. In this publication only parabolic problems are considered. Here lie, mainly, the problems which have been investigated most thoroughly --- the construction of Liapunov functionals which naturally generalize Liapunov functions for nonlinear parabolic equations of the second order with one spatial variable. The authors establish stabilizing solutions theorems, and the necessary and sufficient conditions of general and asymptotic stability of stationary solutions, including the so-called critical case. Attraction domains for stable solutions of mixed problems for these equations are described. Furthermore, estimates for the number of stationary solutions are obtained.
Book Synopsis Linear and Quasilinear Parabolic Systems: Sobolev Space Theory by : David Hoff
Download or read book Linear and Quasilinear Parabolic Systems: Sobolev Space Theory written by David Hoff and published by American Mathematical Soc.. This book was released on 2020-11-18 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a systematic theory of weak solutions in Hilbert-Sobolev spaces of initial-boundary value problems for parabolic systems of partial differential equations with general essential and natural boundary conditions and minimal hypotheses on coefficients. Applications to quasilinear systems are given, including local existence for large data, global existence near an attractor, the Leray and Hopf theorems for the Navier-Stokes equations and results concerning invariant regions. Supplementary material is provided, including a self-contained treatment of the calculus of Sobolev functions on the boundaries of Lipschitz domains and a thorough discussion of measurability considerations for elements of Bochner-Sobolev spaces. This book will be particularly useful both for researchers requiring accessible and broadly applicable formulations of standard results as well as for students preparing for research in applied analysis. Readers should be familiar with the basic facts of measure theory and functional analysis, including weak derivatives and Sobolev spaces. Prior work in partial differential equations is helpful but not required.
Book Synopsis The Regularity of General Parabolic Systems with Degenerate Diffusion by : Verena Bögelein
Download or read book The Regularity of General Parabolic Systems with Degenerate Diffusion written by Verena Bögelein and published by American Mathematical Soc.. This book was released on 2013-01-28 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the paper is twofold. On one hand the authors want to present a new technique called $p$-caloric approximation, which is a proper generalization of the classical compactness methods first developed by DeGiorgi with his Harmonic Approximation Lemma. This last result, initially introduced in the setting of Geometric Measure Theory to prove the regularity of minimal surfaces, is nowadays a classical tool to prove linearization and regularity results for vectorial problems. Here the authors develop a very far reaching version of this general principle devised to linearize general degenerate parabolic systems. The use of this result in turn allows the authors to achieve the subsequent and main aim of the paper, that is, the implementation of a partial regularity theory for parabolic systems with degenerate diffusion of the type $\partial_t u - \mathrm{div} a(Du)=0$, without necessarily assuming a quasi-diagonal structure, i.e. a structure prescribing that the gradient non-linearities depend only on the the explicit scalar quantity.
Book Synopsis Nonlinear Parabolic Equations and Hyperbolic-Parabolic Coupled Systems by : Songmu Zheng
Download or read book Nonlinear Parabolic Equations and Hyperbolic-Parabolic Coupled Systems written by Songmu Zheng and published by CRC Press. This book was released on 2019-12-02 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the global existence, uniqueness and asymptotic behaviour of smooth solutions to both initial value problems and initial boundary value problems for nonlinear parabolic equations and hyperbolic parabolic coupled systems. Most of the material is based on recent research carried out by the author and his collaborators. The book can be divided into two parts. In the first part, the results on decay of solutions to nonlinear parabolic equations and hyperbolic parabolic coupled systems are obtained, and a chapter is devoted to the global existence of small smooth solutions to fully nonlinear parabolic equations and quasilinear hyperbolic parabolic coupled systems. Applications of the results to nonlinear thermoelasticity and fluid dynamics are also shown. Some nonlinear parabolic equations and coupled systems arising from the study of phase transitions are investigated in the second part of the book. The global existence, uniqueness and asymptotic behaviour of smooth solutions with arbitrary initial data are obtained. The final chapter is further devoted to related topics: multiplicity of equilibria and the existence of a global attractor, inertial manifold and inertial set. A knowledge of partial differential equations and Sobolev spaces is assumed. As an aid to the reader, the related concepts and results are collected and the relevant references given in the first chapter. The work will be of interest to researchers and graduate students in pure and applied mathematics, mathematical physics and applied sciences.
Book Synopsis Superlinear Parabolic Problems by : Pavol Quittner
Download or read book Superlinear Parabolic Problems written by Pavol Quittner and published by Springer Science & Business Media. This book was released on 2007-12-16 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology. The book is self-contained and up-to-date, taking special care on the didactical preparation of the material. It is devoted to problems that are intensively studied but have not been treated thus far in depth in the book literature.
Book Synopsis Analytic Semigroups and Optimal Regularity in Parabolic Problems by : Alessandra Lunardi
Download or read book Analytic Semigroups and Optimal Regularity in Parabolic Problems written by Alessandra Lunardi and published by Springer Science & Business Media. This book was released on 2012-12-13 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of parabolic problems. Particular attention is paid to optimal regularity results in linear equations. Furthermore, these results are used to study several other problems, especially fully nonlinear ones. Owing to the new unified approach chosen, known theorems are presented from a novel perspective and new results are derived. The book is self-contained. It is addressed to PhD students and researchers interested in abstract evolution equations and in parabolic partial differential equations and systems. It gives a comprehensive overview on the present state of the art in the field, teaching at the same time how to exploit its basic techniques. - - - This very interesting book provides a systematic treatment of the basic theory of analytic semigroups and abstract parabolic equations in general Banach spaces, and how this theory may be used in the study of parabolic partial differential equations; it takes into account the developments of the theory during the last fifteen years. (...) For instance, optimal regularity results are a typical feature of abstract parabolic equations; they are comprehensively studied in this book, and yield new and old regularity results for parabolic partial differential equations and systems. (Mathematical Reviews) Motivated by applications to fully nonlinear problems the approach is focused on classical solutions with continuous or Hölder continuous derivatives. (Zentralblatt MATH)
Book Synopsis Regularity for Solutions to Parabolic Systems and Nonlocal Minimization Problems by : Joe Geisbauer
Download or read book Regularity for Solutions to Parabolic Systems and Nonlocal Minimization Problems written by Joe Geisbauer and published by . This book was released on 2013 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this dissertation is to contribute to both the nonlocal and the local settings of regularity theory within the calculus of variations. In the nonlocal theory, we first establish the existence of minimizers for two classes of functionals. However, the main result of Chapter 2 states an analogue for higher differentiability of minimizers in the setting of nonlocal functionals, which is established through an application of the difference quotient method. This nonlocal analogue is stated in terms of the fractional order difference quotient, which corresponds to the order of the Besov space to which the solution belongs.
Book Synopsis Parabolic Equations with Irregular Data and Related Issues by : Claude Le Bris
Download or read book Parabolic Equations with Irregular Data and Related Issues written by Claude Le Bris and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-06-17 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the existence and uniqueness of solutions to parabolic-type equations with irregular coefficients and/or initial conditions. It elaborates on the DiPerna-Lions theory of renormalized solutions to linear transport equations and related equations, and also examines the connection between the results on the partial differential equation and the well-posedness of the underlying stochastic/ordinary differential equation.
Book Synopsis Parabolic Systems with Polynomial Growth and Regularity by : Frank Duzaar
Download or read book Parabolic Systems with Polynomial Growth and Regularity written by Frank Duzaar and published by American Mathematical Soc.. This book was released on 2011 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors establish a series of optimal regularity results for solutions to general non-linear parabolic systems $ u_t- \mathrm{div} \ a(x,t,u,Du)+H=0,$ under the main assumption of polynomial growth at rate $p$ i.e. $ a(x,t,u,Du) \leq L(1+ Du ^{p-1}), p \geq 2.$ They give a unified treatment of various interconnected aspects of the regularity theory: optimal partial regularity results for the spatial gradient of solutions, the first estimates on the (parabolic) Hausdorff dimension of the related singular set, and the first Calderon-Zygmund estimates for non-homogeneous problems are achieved here.
Book Synopsis Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations by : Victor A. Galaktionov
Download or read book Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations written by Victor A. Galaktionov and published by CRC Press. This book was released on 2014-09-22 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations. The authors present a unified approach to deal with these quasilinear PDEs.The book
