| Titre : | Partial differential equations : an introduction |
| Auteurs : | Henry Thonier |
| Type de document : | texte imprimé |
| Editeur : | Issy-les-Moulineaux : ESF éd, 1964 |
| Format : | XIII, 263 p. / ill. / 26 cm |
| Note générale : | Trad. de : Partielle Differentialgleichungen. -Bibliogr. at the end of chapiters. -Index |
| Langues : | Français |
| Index. décimale : | 025.12 (Services de reprographie et des publications) |
| Tags : | Differential equations, Partial |
| Résumé : |
This book is intended to give an introduction to the field of partial differential equations. The preentation is intentionally not too brief so that graduate ste=udents should be able to read it without serious difficulty. In addition to requiring a thorough knowledge of differential and integral calulus as well as of the theory of ordinary differential equations, it presupposes a few results from complex variables, and, in ts last part, a few from functional analysis and real variables. |
| Note de contenu : |
Summary :
I. Exemples. 1. Introduction. 2. The wave equation. 3. The potential equation. 4.The geat equation. II. Classification into types, theory of characteristics, and normal form. 1. Differential equations of the first order. 2. Systems of differential equations of the first order. 3. On the ncessity of classification into types. III. Questions of uniqueness. 1. Elliptic and elliptic-parabolic type. 2. Parabolic type. 3. Hyperbolic type. 4. Mixed type. IV. Questions of existence. 1. Equations of hyperbolic type in two independent variables. 2. Boundary and initial-value problemes for equations of hyperbolic and parabolic type in two independent variables. 3. Equations of elliptic type. 4. Weyl's lemma for equations of elliptic type. V. Simple tools from functional analysisi applied to questions of existence. 1. Auxiliary tools. 2. Schauder"s technique of proof for existence problèmes in elliptic diffrential equations. 3. The regular eigenvalue problem. 4. Elliptic systems of differential equations. |
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