Existence And Uniqueness Theorems For Partial Differential Equations With Multiple Characteristics
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Existence And Uniqueness Theorems For Partial Differential Equations With Multiple Characteristics
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Author : Marvin Zeman
language : en
Publisher:
Release Date : 1974
Existence And Uniqueness Theorems For Partial Differential Equations With Multiple Characteristics written by Marvin Zeman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mathematics categories.
Existence Theorems In Partial Differential Equations Am 23 Volume 23
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Author : Dorothy L. Bernstein
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Existence Theorems In Partial Differential Equations Am 23 Volume 23 written by Dorothy L. Bernstein and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
The description for this book, Existence Theorems in Partial Differential Equations. (AM-23), Volume 23, will be forthcoming.
The Characteristic Method And Its Generalizations For First Order Nonlinear Partial Differential Equations
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Author : Tran Duc Van
language : en
Publisher: CRC Press
Release Date : 1999-06-25
The Characteristic Method And Its Generalizations For First Order Nonlinear Partial Differential Equations written by Tran Duc Van and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-06-25 with Mathematics categories.
Despite decades of research and progress in the theory of generalized solutions to first-order nonlinear partial differential equations, a gap between the local and the global theories remains: The Cauchy characteristic method yields the local theory of classical solutions. Historically, the global theory has principally depended on the vanishing viscosity method. The authors of this volume help bridge the gap between the local and global theories by using the characteristic method as a basis for setting a theoretical framework for the study of global generalized solutions. That is, they extend the smooth solutions obtained by the characteristic method. The authors offer material previously unpublished in book form, including treatments of the life span of classical solutions, the construction of singularities of generalized solutions, new existence and uniqueness theorems on minimax solutions, differential inequalities of Haar type and their application to the uniqueness of global, semi-classical solutions, and Hopf-type explicit formulas for global solutions. These subjects yield interesting relations between purely mathematical theory and the applications of first-order nonlinear PDEs. The Characteristic Method and Its Generalizations for First-Order Nonlinear Partial Differential Equations represents a comprehensive exposition of the authors' works over the last decade. The book is self-contained and assumes only basic measure theory, topology, and ordinary differential equations as prerequisites. With its innovative approach, new results, and many applications, it will prove valuable to mathematicians, physicists, and engineers and especially interesting to researchers in nonlinear PDEs, differential inequalities, multivalued analysis, differential games, and related topics in applied analysis.
Existence Theorems In Partial Differential Equations
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Author : Dorothy Lewis Bernstein
language : en
Publisher:
Release Date : 1950
Existence Theorems In Partial Differential Equations written by Dorothy Lewis Bernstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1950 with Mathematics categories.
Partial Differential Equations With Multiple Characteristics
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Author : Maria Mascarello
language : en
Publisher: Wiley-VCH
Release Date : 1997-11-03
Partial Differential Equations With Multiple Characteristics written by Maria Mascarello and has been published by Wiley-VCH this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-11-03 with Mathematics categories.
This book is devoted to the general theory of partial differential equations with multiple characteristics. The methods of the microlocal analysis are reviewed and used to prove recent results on local solvability, hypoellipticity, propagation of singularities in the frame of Sobolev spaces, Schwartz distributions, and Gevrey ultradistributions. The Cauchy problem is also considered.
Partial Differential Equations
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Author : Emmanuele DiBenedetto
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-09
Partial Differential Equations written by Emmanuele DiBenedetto and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-09 with Mathematics categories.
This text is meant to be a self-contained, elementary introduction to Partial Differential Equations, assuming only advanced differential calculus and some basic LP theory. Although the basic equations treated in this book, given its scope, are linear, we have made an attempt to approach them from a nonlinear perspective. Chapter I is focused on the Cauchy-Kowaleski theorem. We discuss the notion of characteristic surfaces and use it to classify partial differential equations. The discussion grows out of equations of second order in two variables to equations of second order in N variables to p.d.e.'s of any order in N variables. In Chapters II and III we study the Laplace equation and connected elliptic theory. The existence of solutions for the Dirichlet problem is proven by the Perron method. This method clarifies the structure ofthe sub(super)harmonic functions and is closely related to the modern notion of viscosity solution. The elliptic theory is complemented by the Harnack and Liouville theorems, the simplest version of Schauder's estimates and basic LP -potential estimates. Then, in Chapter III, the Dirichlet and Neumann problems, as well as eigenvalue problems for the Laplacian, are cast in terms of integral equations. This requires some basic facts concerning double layer potentials and the notion of compact subsets of LP, which we present.
Partial Differential Equations
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Author : P. R. Garabedian
language : en
Publisher: American Mathematical Society
Release Date : 2023-10-19
Partial Differential Equations written by P. R. Garabedian and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-19 with Mathematics categories.
From a review of the original edition: This book is primarily a text for a graduate course in partial differential equations, although the later chapters are devoted to special topics not ordinarily covered in books in this field … [T]he author has made use of an interesting combination of classical and modern analysis in his proofs … Because of the author's emphasis on constructive methods for solving problems which are of physical interest, his book will likely be as welcome to the engineer and the physicist as to the mathematician … The author and publisher are to be complimented on the general appearance of the book. —Mathematical Reviews This book is a gem. It fills the gap between the standard introductory material on PDEs that an undergraduate is likely to encounter after a good ODE course (separation of variables, the basics of the second-order equations from mathematical physics) and the advanced methods (such as Sobolev spaces and fixed point theorems) that one finds in modern books. Although this is not designed as a textbook for applied mathematics, the approach is strongly informed by applications. For instance, there are many existence and uniqueness results, but they are usually approached via very concrete techniques. The text contains the standard topics that one expects in an intermediate PDE course: the Dirichlet and Neumann problems, Cauchy's problem, characteristics, the fundamental solution, PDEs in the complex domain, plus a chapter on finite differences, on nonlinear fluid mechanics, and another on integral equations. It is an excellent text for advanced undergraduates or beginning graduate students in mathematics or neighboring fields, such as engineering and physics, where PDEs play a central role.
Existence And Uniqueness Theorem For Partial Differential Equations In Complex Domains
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Author : Detlef Gronau
language : en
Publisher:
Release Date : 1985
Existence And Uniqueness Theorem For Partial Differential Equations In Complex Domains written by Detlef Gronau and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.
An Existence And Uniqueness Theorem For Integro Partial Differential Equations
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Author : Dale Edouard Walston
language : en
Publisher:
Release Date : 1961
An Existence And Uniqueness Theorem For Integro Partial Differential Equations written by Dale Edouard Walston and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Integral equations categories.
Uniqueness And Nonuniqueness Criteria For Ordinary Differential Equations
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Author : Ratan Prakash Agarwal
language : en
Publisher: World Scientific
Release Date : 1993
Uniqueness And Nonuniqueness Criteria For Ordinary Differential Equations written by Ratan Prakash Agarwal and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
This monograph aims to fill a void by making available a source book which first systematically describes all the available uniqueness and nonuniqueness criteria for ordinary differential equations, and compares and contrasts the merits of these criteria, and second, discusses open problems and offers some directions towards possible solutions.