Partial Differential Equations With Multiple Characteristics
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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.
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.
On Cauchy S Problem For Partial Differential Equations With Multiple Characteristics
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Author : Anneli Lax
language : en
Publisher:
Release Date : 1956
On Cauchy S Problem For Partial Differential Equations With Multiple Characteristics written by Anneli Lax and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1956 with Mathematics categories.
Methods For Partial Differential Equations
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Author : Marcelo R. Ebert
language : en
Publisher: Birkhäuser
Release Date : 2018-02-23
Methods For Partial Differential Equations written by Marcelo R. Ebert and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-23 with Mathematics categories.
This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the “research project for beginners” proposed at the end of the book. It is a valuable resource for advanced graduates and undergraduate students who are interested in specializing in this area. The book is organized in five parts: In Part 1 the authors review the basics and the mathematical prerequisites, presenting two of the most fundamental results in the theory of partial differential equations: the Cauchy-Kovalevskaja theorem and Holmgren's uniqueness theorem in its classical and abstract form. It also introduces the method of characteristics in detail and applies this method to the study of Burger's equation. Part 2 focuses on qualitative properties of solutions to basic partial differential equations, explaining the usual properties of solutions to elliptic, parabolic and hyperbolic equations for the archetypes Laplace equation, heat equation and wave equation as well as the different features of each theory. It also discusses the notion of energy of solutions, a highly effective tool for the treatment of non-stationary or evolution models and shows how to define energies for different models. Part 3 demonstrates how phase space analysis and interpolation techniques are used to prove decay estimates for solutions on and away from the conjugate line. It also examines how terms of lower order (mass or dissipation) or additional regularity of the data may influence expected results. Part 4 addresses semilinear models with power type non-linearity of source and absorbing type in order to determine critical exponents: two well-known critical exponents, the Fujita exponent and the Strauss exponent come into play. Depending on concrete models these critical exponents divide the range of admissible powers in classes which make it possible to prove quite different qualitative properties of solutions, for example, the stability of the zero solution or blow-up behavior of local (in time) solutions. The last part features selected research projects and general background material.
Partial Differential Equations
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Author : Bhamra
language : en
Publisher: PHI Learning Pvt. Ltd.
Release Date : 2010-01-30
Partial Differential Equations written by Bhamra and has been published by PHI Learning Pvt. Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-30 with Mathematics categories.
and postgraduate (MA/MSc) students of mathematics, and conforms to the course curriculum prescribed by UGC. The text is broadly organized into two parts. The first part (Lessons 1 to 15) mostly covers the first-order equations in two variables. In these lessons, the mathematical importance of PDEs of first order in physics and applied sciences has also been highlighted. The other part (Lessons 16 to 50) deals with the various properties of second-order and first- order PDEs. The book emphasizes the applications of PDEs and covers various important topics such as the Hamilton Jacobi equation, Conservation laws, Similarity solution, Asymptotics and Power series solution and many more. The graded problems, the techniques for solving them, and a large number of exercises with hints and answers help students gain the necessary skill and confidence in handling the subject.
Solvability And Hypoellipticity For Semilinear Partial Differential Equations With Multiple Characteristics
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Author : Alessandro Oliaro
language : en
Publisher:
Release Date : 2000
Solvability And Hypoellipticity For Semilinear Partial Differential Equations With Multiple Characteristics written by Alessandro Oliaro and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
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.
The Uniqueness Of The Cauchy Problem For Partial Differential Equations Whih May Have Multiple Characteristics
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Author : Peter Mike Goorjian
language : en
Publisher:
Release Date : 1969
The Uniqueness Of The Cauchy Problem For Partial Differential Equations Whih May Have Multiple Characteristics written by Peter Mike Goorjian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with categories.
The Cauchy Problem For Hyperbolic Operators
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Author : Karen Yagdjian
language : en
Publisher: De Gruyter Akademie Forschung
Release Date : 1997
The Cauchy Problem For Hyperbolic Operators written by Karen Yagdjian and has been published by De Gruyter Akademie Forschung this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Partial Differential Equations
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Author : Todor V. Gramchev
language : en
Publisher: Wiley-VCH
Release Date : 2000-02-22
Partial Differential Equations written by Todor V. Gramchev and has been published by Wiley-VCH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-22 with Mathematics categories.
The applications of methods from microlocal analysis for PDE have been a fast developing area during the last years. The authors, both are well known in the community, publish for the first time some of their research results in a summarized form. The essential point of the approach is the use of the various types of approximate (asymptotic) solutions in the study of differential equations in the smooth and the Gevrey spaces. In this volume, the authors deal with the following themes: Microlocal properties of pseudodifferential operators with multiple characteristics of involutive type in the framework of the Sobolev spaces; Abstract schemes for constructing approximate solutions to linear partial differential equations with characteristics of constant multiplicity m greater than or equal 2 in the framework of Gevrey spaces; Local solvability, hypoellipticity and singular solutions in Gevrey spaces; Global Gevrey solvability on the torus for linear partial differential equations; Applications of asymptotic methods for local (non)solvability for quasihomogeneous operators; Applications of Airy asymptotic solutions to degenerate oblique derivative problems for second order strictly hyperbolic equations; Approximate Gevrey normal forms of analytic involutions and analytic glancing hypersurfaces with applications for effective stability estimates for billiard ball maps.