Mizohata / Ames On the Cauchy Problem

1. Auflage 2014
ISBN: 978-1-4832-6906-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 186 Seiten, Web PDF

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 Schr”dinger 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.

Autoren/Hrsg.

Mizohata, Sigeru

Ames, William F.

Inhaltsverzeichnis

1;Front Cover;1
2;On the Cauchy Problem;4
3;Copyright Page;5
4;Table of Contents;8
5;Lecture I. Evolution Equations ;10
5.1;Comments;17
5.2;References;18
6;Lecture II. H8-wellposedness ;20
6.1;Appendix ;29
6.2;References;36
7;Lecture III. Lax-Mizohata Theorem ;37
7.1;§ 1. Let P(x,t; .x, .t) be Kowalewskian. Namely ;37
7.2;§ 2. We explain here some basic facts concerning pseudo-differential;42
7.3;§ 3. Proof of Theorem 3;44
7.4;§ 4. What about the proof of Theorem 2 ?;50
7.5;§ 5. Further considerations;54
7.6;Appendix;58
7.7;References;68
8;Lecture IV. Cauchy Problems in Gevrey Class;69
8.1;§ 1. Introduction and results;69
8.2;§ 2. Fundamental proposition;78
8.3;§ 3. Proof of Theorem 4;84
8.4;§ 4. Gevrey property in t of solutions;90
8.5;§ 5. Comments ;94
8.6;Appendix;95
8.7;References;104
9;Lecture V. Micro-local Analysis in Gevrey Class;106
9.1;§ 1 Introduction ;106
9.2;§ 2. Definition of {an (D), ßn(x)};113
9.3;§ 3. Criterion of WFs(u) by Sn;117
9.4;§ 4. Some comments on WF(u);120
9.5;§ 5. Some comments on WFA(u);124
9.6;Appendix;127
10;Lecture VI. Micro-local Analysis in Gevrey Class (II);144
10.1;§ 1 Preliminaries ;144
10.2;§ 2 Proof of Theorem 1;147
10.3;§ 3. Some consequence of Theorem 1;154
10.4;§ 4 Propagation of singularities in the sense of C8;159
10.5;Appendix;169
11;Lecture VII. Schrödinger Type Equations;175
11.1;§ 1. Introduction (General view-points on evolution equations);175
11.2;§ 2. Necessity of (C0);179
11.3;§ 3. Sufficiency for L2-wellposedness;182
11.4;References;186