Uniformly Bounded Solutions Of Quasilinear Parabolic Systems

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Linear and Quasilinear Parabolic Systems: Sobolev Space Theory

Author : David Hoff
Publisher : American Mathematical Soc.
ISBN 13 : 1470461617
Total Pages : 226 pages
Book Rating : 4.4/5 (74 download)

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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.

Semigroup Theory and Evolution Equations

Author : Philippe Clement
Publisher : CRC Press
ISBN 13 : 1000946525
Total Pages : 544 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Semigroup Theory and Evolution Equations by : Philippe Clement

Download or read book Semigroup Theory and Evolution Equations written by Philippe Clement and published by CRC Press. This book was released on 2023-05-31 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Second International Conference on Trends in Semigroup Theory and Evolution Equations held Sept. 1989, Delft University of Technology, the Netherlands. Papers deal with recent developments in semigroup theory (e.g., positive, dual, integrated), and nonlinear evolution equations (e

Large Time Behavior of Solutions for General Quasilinear Hyperbolic-Parabolic Systems of Conservation Laws

Author : Tai-Ping Liu
Publisher : American Mathematical Soc.
ISBN 13 : 0821805452
Total Pages : 135 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Large Time Behavior of Solutions for General Quasilinear Hyperbolic-Parabolic Systems of Conservation Laws by : Tai-Ping Liu

Download or read book Large Time Behavior of Solutions for General Quasilinear Hyperbolic-Parabolic Systems of Conservation Laws written by Tai-Ping Liu and published by American Mathematical Soc.. This book was released on 1997 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: We are interested in the time-asymptotic behavior of solutions to viscous conservation laws. Through the pointwise estimates for the Green's function of the linearized system and the analysis of coupling of nonlinear diffusion waves, we obtain explicit expressions of the time-asymptotic behavior of the solutions. This yields optimal estimates in the integral norms. For most physical models, the viscosity matrix is not positive definite and the system is hyperbolic-parabolic, and not uniformly parabolic. This implies that the Green's function may contain Dirac [lowercase Greek]Delta-functions. When the corresponding inviscid system is non-strictly hyperbolic, the time-asymptotic state contains generalized Burgers solutions. These are illustrated by applying our general theory to the compressible Navier-Stokes equations and the equations of magnetohydrodynamics.

Blow-Up in Quasilinear Parabolic Equations

Author : A. A. Samarskii
Publisher : Walter de Gruyter
ISBN 13 : 3110889862
Total Pages : 561 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Blow-Up in Quasilinear Parabolic Equations by : A. A. Samarskii

Download or read book Blow-Up in Quasilinear Parabolic Equations written by A. A. Samarskii and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Linear and Nonlinear Parabolic Complex Equations

Author : Guo Chun Wen
Publisher : World Scientific
ISBN 13 : 9789810238568
Total Pages : 260 pages
Book Rating : 4.2/5 (385 download)

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Book Synopsis Linear and Nonlinear Parabolic Complex Equations by : Guo Chun Wen

Download or read book Linear and Nonlinear Parabolic Complex Equations written by Guo Chun Wen and published by World Scientific. This book was released on 1999 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is a very interesting book written by a well-known expert on complex methods in partial differential equations. It contains many recent results, many of them published for the first time, some published originally in Chinese".Mathematical Reviews

Transport Equations in Biology

Author : Benoît Perthame
Publisher : Springer Science & Business Media
ISBN 13 : 3764378425
Total Pages : 206 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Transport Equations in Biology by : Benoît Perthame

Download or read book Transport Equations in Biology written by Benoît Perthame and published by Springer Science & Business Media. This book was released on 2006-12-14 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents models written as partial differential equations and originating from various questions in population biology, such as physiologically structured equations, adaptive dynamics, and bacterial movement. Its purpose is to derive appropriate mathematical tools and qualitative properties of the solutions. The book further contains many original PDE problems originating in biosciences.

Moving Interfaces and Quasilinear Parabolic Evolution Equations

Author : Jan Prüss
Publisher : Birkhäuser
ISBN 13 : 3319276980
Total Pages : 618 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Moving Interfaces and Quasilinear Parabolic Evolution Equations by : Jan Prüss

Download or read book Moving Interfaces and Quasilinear Parabolic Evolution Equations written by Jan Prüss and published by Birkhäuser. This book was released on 2016-07-25 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions, and an exposition of the geometry of moving hypersurfaces.

Parabolic Systems with Polynomial Growth and Regularity

Author : Frank Duzaar
Publisher : American Mathematical Soc.
ISBN 13 : 0821849670
Total Pages : 135 pages
Book Rating : 4.8/5 (218 download)

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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.

Second Order Parabolic Differential Equations

Author : Gary M. Lieberman
Publisher : World Scientific
ISBN 13 : 9789810228835
Total Pages : 472 pages
Book Rating : 4.2/5 (288 download)

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Book Synopsis Second Order Parabolic Differential Equations by : Gary M. Lieberman

Download or read book Second Order Parabolic Differential Equations written by Gary M. Lieberman and published by World Scientific. This book was released on 1996 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction. Maximum principles. Introduction to the theory of weak solutions. Hölder estimates. Existence, uniqueness, and regularity of solutions. Further theory of weak solutions. Strong solutions. Fixed point theorems and their applications. Comparison and maximum principles. Boundary gradient estimates. Global and local gradient bounds. Hölder gradient estimates and existence theorems. The oblique derivative problem for quasilinear parabolic equations. Fully nonlinear equations. Introduction. Monge-Ampère and Hessian equations.

Distributions, Sobolev Spaces, Elliptic Equations

Author : Dorothee Haroske
Publisher : European Mathematical Society
ISBN 13 : 9783037190425
Total Pages : 312 pages
Book Rating : 4.1/5 (94 download)

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Book Synopsis Distributions, Sobolev Spaces, Elliptic Equations by : Dorothee Haroske

Download or read book Distributions, Sobolev Spaces, Elliptic Equations written by Dorothee Haroske and published by European Mathematical Society. This book was released on 2007 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is the main aim of this book to develop at an accessible, moderate level an $L_2$ theory for elliptic differential operators of second order on bounded smooth domains in Euclidean n-space, including a priori estimates for boundary-value problems in terms of (fractional) Sobolev spaces on domains and on their boundaries, together with a related spectral theory. The presentation is preceded by an introduction to the classical theory for the Laplace-Poisson equation, and some chapters provide required ingredients such as the theory of distributions, Sobolev spaces and the spectral theory in Hilbert spaces. The book grew out of two-semester courses the authors have given several times over a period of ten years at the Friedrich Schiller University of Jena. It is addressed to graduate students and mathematicians who have a working knowledge of calculus, measure theory and the basic elements of functional analysis (as usually covered by undergraduate courses) and who are seeking an accessible introduction to some aspects of the theory of function spaces and its applications to elliptic equations.

Linear and Quasi-linear Equations of Parabolic Type

Author : Olʹga A. Ladyženskaja
Publisher : American Mathematical Soc.
ISBN 13 : 9780821815731
Total Pages : 74 pages
Book Rating : 4.8/5 (157 download)

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Book Synopsis Linear and Quasi-linear Equations of Parabolic Type by : Olʹga A. Ladyženskaja

Download or read book Linear and Quasi-linear Equations of Parabolic Type written by Olʹga A. Ladyženskaja and published by American Mathematical Soc.. This book was released on 1988 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt: Equations of parabolic type are encountered in many areas of mathematics and mathematical physics, and those encountered most frequently are linear and quasi-linear parabolic equations of the second order. In this volume, boundary value problems for such equations are studied from two points of view: solvability, unique or otherwise, and the effect of smoothness properties of the functions entering the initial and boundary conditions on the smoothness of the solutions.

Nonlinear partial differential equations in differential geometry

Author : Robert Hardt
Publisher : American Mathematical Soc.
ISBN 13 : 9780821804315
Total Pages : 356 pages
Book Rating : 4.8/5 (43 download)

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Book Synopsis Nonlinear partial differential equations in differential geometry by : Robert Hardt

Download or read book Nonlinear partial differential equations in differential geometry written by Robert Hardt and published by American Mathematical Soc.. This book was released on 1996 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains lecture notes of minicourses at the Regional Geometry Institute at Park City, Utah, in July 1992. Presented here are surveys of breaking developments in a number of areas of nonlinear partial differential equations in differential geometry. The authors of the articles are not only excellent expositors, but are also leaders in this field of research. All of the articles provide in-depth treatment of the topics and require few prerequisites and less background than current research articles.

Lecture Notes in Pure and Applied Mathematics

Author :
Publisher :
ISBN 13 :
Total Pages : 994 pages
Book Rating : 4.:/5 (51 download)

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Book Synopsis Lecture Notes in Pure and Applied Mathematics by :

Download or read book Lecture Notes in Pure and Applied Mathematics written by and published by . This book was released on 1991 with total page 994 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Linear and Quasi-linear Equations of Parabolic Type

Author : Olʹga Aleksandrovna Ladyzhenskai͡a
Publisher : American Mathematical Soc.
ISBN 13 : 9780821886533
Total Pages : 670 pages
Book Rating : 4.8/5 (865 download)

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Book Synopsis Linear and Quasi-linear Equations of Parabolic Type by : Olʹga Aleksandrovna Ladyzhenskai͡a

Download or read book Linear and Quasi-linear Equations of Parabolic Type written by Olʹga Aleksandrovna Ladyzhenskai͡a and published by American Mathematical Soc.. This book was released on 1968 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Proceedings of the First International Forum on Financial Mathematics and Financial Technology

Author : Zhiyong Zheng
Publisher : Springer Nature
ISBN 13 : 9811583730
Total Pages : 238 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Proceedings of the First International Forum on Financial Mathematics and Financial Technology by : Zhiyong Zheng

Download or read book Proceedings of the First International Forum on Financial Mathematics and Financial Technology written by Zhiyong Zheng and published by Springer Nature. This book was released on 2021-02-08 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains high-quality papers presented at the First International Forum on Financial Mathematics and Financial Technology. With the rapid development of FinTech, the in-depth integration between mathematics, finance and advanced technology is the general trend. This book focuses on selected aspects of the current and upcoming trends in FinTech. In detail, the included scientific papers focus on financial mathematics and FinTech, presenting the innovative mathematical models and state-of-the-art technologies such as deep learning, with the aim to improve our financial analysis and decision-making and enhance the quality of financial services and risk control. The variety of the papers delivers added value for both scholars and practitioners where they will find perfect integration of elegant mathematical models and up-to-date data mining technologies in financial market analysis.

Evolution Equations, Semigroups and Functional Analysis

Author : Brunello Terreni
Publisher : Springer Science & Business Media
ISBN 13 : 9783764367916
Total Pages : 426 pages
Book Rating : 4.3/5 (679 download)

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Book Synopsis Evolution Equations, Semigroups and Functional Analysis by : Brunello Terreni

Download or read book Evolution Equations, Semigroups and Functional Analysis written by Brunello Terreni and published by Springer Science & Business Media. This book was released on 2002 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brunello Terreni (1953-2000) was a researcher and teacher with vision and dedication. The present volume is dedicated to the memory of Brunello Terreni. His mathematical interests are reflected in 20 expository articles written by distinguished mathematicians. The unifying theme of the articles is "evolution equations and functional analysis", which is presented in various and diverse forms: parabolic equations, semigroups, stochastic evolution, optimal control, existence, uniqueness and regularity of solutions, inverse problems as well as applications. Contributors: P. Acquistapace, V. Barbu, A. Briani, L. Boccardo, P. Colli Franzone, G. Da Prato, D. Donatelli, A. Favini, M. Fuhrmann, M. Grasselli, R. Illner, H. Koch, R. Labbas, H. Lange, I. Lasiecka, A. Lorenzi, A. Lunardi, P. Marcati, R. Nagel, G. Nickel, V. Pata, M. M. Porzio, B. Ruf, G. Savaré, R. Schnaubelt, E. Sinestrari, H. Tanabe, H. Teismann, E. Terraneo, R. Triggiani, A. Yagi

Quasilinear Hyperbolic Systems And Dissipative Mechanisms

Author : Ling Hsiao
Publisher : World Scientific
ISBN 13 : 9814497185
Total Pages : 233 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Quasilinear Hyperbolic Systems And Dissipative Mechanisms by : Ling Hsiao

Download or read book Quasilinear Hyperbolic Systems And Dissipative Mechanisms written by Ling Hsiao and published by World Scientific. This book was released on 1998-02-24 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the recent developments in the subject of quasilinear hyperbolic systems with dissipation, such as frictional damping, relaxation, viscosity and heat diffusion. The mathematical theory behind this subject is emphasized in two ways. One emphasis is based on understanding the influence of the dissipation mechanism on the qualitative behavior of solutions, such as the nonlinear diffusive phenomena caused by damping, and other phenomena (including phase transition) for the case with viscosity and heat diffusion. The second emphasis is to take the systems with the dissipation mechanism as an approach to approximating the corresponding system of quasilinear hyperbolic conservation laws - the zero-limit relaxation, or the zero-limit viscosity, and the related topic of nonlinear stability of waves.