Author: Anneli LaxPublisher:
ISBN:
Category : Mathematics
Languages : en
Pages :
Book Description
On Cauchy's Problem for Partial Differential Equations with Multiple Characteristics
Author: Anneli LaxThe Uniqueness of the Cauchy Problem for Partial Differential Equations Whih May Have Multiple Characteristics
Author: Peter Mike GoorjianPartial Differential Equations with Multiple Characteristics
Author: Maria MascarelloPublisher: Wiley-VCH
ISBN:
Category : Mathematics
Languages : en
Pages : 360
Book Description
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.
The Cauchy Problem for Hyperbolic Operators
Author: Karen YagdjianPublisher: De Gruyter Akademie Forschung
ISBN:
Category : Mathematics
Languages : en
Pages : 408
Book Description
Cauchy Problems for Linear Partial Differential Equations with Variable Multiple Characteristics
Author: 瓜生等Lectures on Cauchy's Problem in Linear Partial Differential Equations
Author: Jacques HadamardPublisher:
ISBN:
Category : Cauchy problem
Languages : en
Pages : 336
Book Description
Partial Differential Equations
Author: BhamraPublisher: PHI Learning Pvt. Ltd.
ISBN: 8120339177
Category : Mathematics
Languages : en
Pages : 580
Book Description
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.
Partial Differential Equations
Author: Fritz JohnPublisher: Springer Science & Business Media
ISBN: 0387906096
Category : Mathematics
Languages : en
Pages : 266
Book Description
This book is a very well-accepted introduction to the subject. In it, the author identifies the significant aspects of the theory and explores them with a limited amount of machinery from mathematical analysis. Now, in this fourth edition, the book has again been updated with an additional chapter on Lewy’s example of a linear equation without solutions.
Partial Differential Equations
Author: F. JohnPublisher: Springer Science & Business Media
ISBN: 1461599792
Category : Mathematics
Languages : en
Pages : 258
Book Description
These Notes grew out of a course given by the author in 1952-53. Though the field of Partial Differential Equations has changed considerably since those days, particularly under the impact of methods taken from Functional Analysis, the author feels that the introductory material offered here still is basic for an understanding of the subject. It supplies the necessary intuitive foundation which motivates and anticipates abstract formulations of the questions and relates them to the description of natual phenomena. Added to this second corrected edition is a collection of problems and solutions, which illustrate and supplement the theories developed in the text. Fritz John New York September, 1974 vii TABLE OF CONTENTS Introd uction 1 CHAPrER I - THE SINGLE FIRST ORDER EQUATION 1. The linear and quasi-linear equations. 6 2. The general first order equation for a function of two variables. • • • • • • • • • 15 The general first order equation for a function 3. of n independent variables. • • • • • 37 CHAPrER II - THE CAUCHY PROBLEM FOR HIGHER ORDER EQUATIONS 1. Analytic functions of several real variables • 48 2. Formulation of the Cauchy problem. The notion of characteristics. • • • 54 3. The Cauchy problem for the general non-linear equation ••• 71 4. The Cauchy-Kowalewsky theorem. 76 CHAPTER III - SECOND ORDER EQUATIONS WITH CONSTANT COEFFICIENTS 1. Equations in two independent variables.
Partial Differential Equations
Author: Emmanuele DiBenedettoPublisher: Springer Science & Business Media
ISBN: 1489928405
Category : Mathematics
Languages : en
Pages : 430
Book Description
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.