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On the Cauchy Problem
- 1st Edition - May 10, 2014
- Author: Sigeru Mizohata
- Editor: William F. Ames
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 6 9 0 6 - 1
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… Read more
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Request a sales quoteNotes 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.
Lecture I Evolution EquationsLecture II H∞-wellposednessAppendixLecture III Lax-Mizohata Theorem § 1 § 2 § 3 Proof of Theorem § 4 § 5 Further ConsiderationsAppendix § 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.7Lecture 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 CommentsAppendix § A.1 Proof of Lemma 4 § A.2 Proof of Lemmas 1,2 and 6 § A.3 Proof Lemma 3Lecture 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.1Lecture 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 2Lecture V I I Schrödinger Type Equations § 1 Introduction (General View-Points on Evolution Equations) § 2 Necessity of (Co) § 3 Sufficiency for L2-Wellposedness
- No. of pages: 186
- Language: English
- Edition: 1
- Published: May 10, 2014
- Imprint: Academic Press
- eBook ISBN: 9781483269061
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