On the Cauchy Problem - 1st Edition - ISBN: 9780125016605, 9781483269061

On the Cauchy Problem

1st Edition

Editors: William F. Ames
Authors: Sigeru Mizohata
eBook ISBN: 9781483269061
Imprint: Academic Press
Published Date: 26th August 1986
Page Count: 186
Sales tax will be calculated at check-out Price includes VAT/GST
25% off
25% off
25% off
25% off
25% off
20% off
20% off
25% off
25% off
25% off
25% off
25% off
20% off
20% off
25% off
25% off
25% off
25% off
25% off
20% off
20% off
24.95
18.71
18.71
18.71
18.71
18.71
19.96
19.96
31.95
23.96
23.96
23.96
23.96
23.96
25.56
25.56
19.99
14.99
14.99
14.99
14.99
14.99
15.99
15.99
Unavailable
Price includes VAT/GST
× DRM-Free

Easy - Download and start reading immediately. There’s no activation process to access eBooks; all eBooks are fully searchable, and enabled for copying, pasting, and printing.

Flexible - Read on multiple operating systems and devices. Easily read eBooks on smart phones, computers, or any eBook readers, including Kindle.

Open - Buy once, receive and download all available eBook formats, including PDF, EPUB, and Mobi (for Kindle).

Institutional Access

Secure Checkout

Personal information is secured with SSL technology.

Free Shipping

Free global shipping
No minimum order.

Description

Notes and Reports in Mathematics in Science and Engineering, Volume 3: On the Cauchy Problem focuses on the processes, methodologies, and mathematical approaches to Cauchy problems.

The publication first elaborates on evolution equations, Lax-Mizohata theorem, and Cauchy problems in Gevrey class. Discussions focus on fundamental proposition, proof of theorem 4, Gevrey property in t of solutions, basic facts on pseudo-differential, and proof of theorem 3. The book then takes a look at micro-local analysis in Gevrey class, including proof and consequences of theorem 1. The manuscript examines Schrödinger type equations, as well as general view-points on evolution equations. Numerical representations and analyses are provided in the explanation of these type of equations.

The book is a valuable reference for mathematicians and researchers interested in the Cauchy problem.

Table of Contents


Lecture I Evolution Equations

Lecture II H∞-wellposedness

Appendix

Lecture III Lax-Mizohata Theorem

§ 1

§ 2

§ 3 Proof of Theorem

§ 4

§ 5 Further Considerations

Appendix

§ A.1 Preliminaries

§ A.2 Proof of (12)

§ A.3 Partition of Unity

§ A.4 Estimates of αn(D)b(x,D)χn ±(D)

§ A.5 Proof of (9), (10), (11)

§ A.6

§ A.7

Lecture IV Cauchy Problems in Gevrey Class

§ 1 Introduction and Results

§ 2 Fundamental Proposition

§ 3 Proof of Theorem 4

§ 4 Gevrey Property in t of Solutions

§ 5 Comments

Appendix

§ A.1 Proof of Lemma 4

§ A.2 Proof of Lemmas 1,2 and 6

§ A.3 Proof Lemma 3

Lecture V Micro-local Analysis in Gevrey Class (I)

§ 1 Introduction

§ 2 Definition of {αn(D),βn(X)}

§ 3 Criterion of WFs(u) by Sn

§ 4 Some Comments on WF(u)

§ 5 Some comments on WFA(u)

Appendix

§ A.1 Partition of Unity

§ A.2 Proof of Theorem 1

§ A.3 Proof of (18)

§ A.4 Pseudo-Local Property in y(s)

§ A.5 Proof of Theorem A.1

Lecture VI Micro-local Analysis in Gevrey Class (II)

§ 1 Preliminaries

§ 2 Proof of Theorem 1

§ 3 Some Consequence of Theorem 1

§ 4 Propagation of Singularities in the sense of C∞

Appendix

§ A.1

§ A.2 Proof of Lemma 2

Lecture V I I Schrödinger Type Equations

§ 1 Introduction (General View-Points on Evolution Equations)

§ 2 Necessity of (Co)

§ 3 Sufficiency for L2-Wellposedness

Details

No. of pages:
186
Language:
English
Copyright:
© Academic Press 1985
Published:
Imprint:
Academic Press
eBook ISBN:
9781483269061

About the Editor

William F. Ames

About the Author

Sigeru Mizohata

Ratings and Reviews