Partial Differential Equations and Boundary Value Problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1998
|
| Schriftenreihe: | Mathematics and Its Applications
441 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The material of the present book has been used for graduate-level courses at the University of Ia~i during the past ten years. It is a revised version of a book which appeared in Romanian in 1993 with the Publishing House of the Romanian Academy. The book focuses on classical boundary value problems for the principal equations of mathematical physics: second order elliptic equations (the Poisson equations), heat equations and wave equations. The existence theory of second order elliptic boundary value problems was a great challenge for nineteenth century mathematics and its development was marked by two decisive steps. Undoubtedly, the first one was the Fredholm proof in 1900 of the existence of solutions to Dirichlet and Neumann problems, which represented a triumph of the classical theory of partial differential equations. The second step is due to S. 1. Sobolev (1937) who introduced the concept of weak solution in partial differential equations and inaugurated the modern theory of boundary value problems. The classical theory which is a product ofthe nineteenth century, is concerned with smooth (continuously differentiable) sollutions and its methods rely on classical analysis and in particular on potential theory. The modern theory concerns distributional (weak) solutions and relies on analysis of Sob ole v spaces and functional methods. The same distinction is valid for the boundary value problems associated with heat and wave equations. Both aspects of the theory are present in this book though it is not exhaustive in any sense |
| Beschreibung: | 1 Online-Ressource (XII, 284 p) |
| ISBN: | 9789401591171 9789048150281 |
| DOI: | 10.1007/978-94-015-9117-1 |
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Datensatz im Suchindex
| _version_ | 1804153100691308544 |
|---|---|
| any_adam_object | |
| author | Barbu, Viorel |
| author_facet | Barbu, Viorel |
| author_role | aut |
| author_sort | Barbu, Viorel |
| author_variant | v b vb |
| building | Verbundindex |
| bvnumber | BV042424115 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1184484680 (DE-599)BVBBV042424115 |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-015-9117-1 |
| format | Electronic eBook |
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| id | DE-604.BV042424115 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401591171 9789048150281 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859532 |
| oclc_num | 1184484680 |
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| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XII, 284 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1998 |
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| publisher | Springer Netherlands |
| record_format | marc |
| series2 | Mathematics and Its Applications |
| spelling | Barbu, Viorel Verfasser aut Partial Differential Equations and Boundary Value Problems by Viorel Barbu Dordrecht Springer Netherlands 1998 1 Online-Ressource (XII, 284 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 441 The material of the present book has been used for graduate-level courses at the University of Ia~i during the past ten years. It is a revised version of a book which appeared in Romanian in 1993 with the Publishing House of the Romanian Academy. The book focuses on classical boundary value problems for the principal equations of mathematical physics: second order elliptic equations (the Poisson equations), heat equations and wave equations. The existence theory of second order elliptic boundary value problems was a great challenge for nineteenth century mathematics and its development was marked by two decisive steps. Undoubtedly, the first one was the Fredholm proof in 1900 of the existence of solutions to Dirichlet and Neumann problems, which represented a triumph of the classical theory of partial differential equations. The second step is due to S. 1. Sobolev (1937) who introduced the concept of weak solution in partial differential equations and inaugurated the modern theory of boundary value problems. The classical theory which is a product ofthe nineteenth century, is concerned with smooth (continuously differentiable) sollutions and its methods rely on classical analysis and in particular on potential theory. The modern theory concerns distributional (weak) solutions and relies on analysis of Sob ole v spaces and functional methods. The same distinction is valid for the boundary value problems associated with heat and wave equations. Both aspects of the theory are present in this book though it is not exhaustive in any sense Mathematics Differential equations, partial Potential theory (Mathematics) Mathematical optimization Partial Differential Equations Applications of Mathematics Potential Theory Calculus of Variations and Optimal Control; Optimization Mathematik Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd rswk-swf Elliptisches Randwertproblem (DE-588)4193399-0 gnd rswk-swf Parabolisches Randwertproblem (DE-588)4319434-5 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Wellengleichung (DE-588)4065315-8 gnd rswk-swf Wellengleichung (DE-588)4065315-8 s Randwertproblem (DE-588)4048395-2 s 1\p DE-604 Lineare partielle Differentialgleichung (DE-588)4167708-0 s 2\p DE-604 Parabolisches Randwertproblem (DE-588)4319434-5 s 3\p DE-604 Elliptisches Randwertproblem (DE-588)4193399-0 s 4\p DE-604 https://doi.org/10.1007/978-94-015-9117-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Barbu, Viorel Partial Differential Equations and Boundary Value Problems Mathematics Differential equations, partial Potential theory (Mathematics) Mathematical optimization Partial Differential Equations Applications of Mathematics Potential Theory Calculus of Variations and Optimal Control; Optimization Mathematik Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd Parabolisches Randwertproblem (DE-588)4319434-5 gnd Randwertproblem (DE-588)4048395-2 gnd Wellengleichung (DE-588)4065315-8 gnd |
| subject_GND | (DE-588)4167708-0 (DE-588)4193399-0 (DE-588)4319434-5 (DE-588)4048395-2 (DE-588)4065315-8 |
| title | Partial Differential Equations and Boundary Value Problems |
| title_auth | Partial Differential Equations and Boundary Value Problems |
| title_exact_search | Partial Differential Equations and Boundary Value Problems |
| title_full | Partial Differential Equations and Boundary Value Problems by Viorel Barbu |
| title_fullStr | Partial Differential Equations and Boundary Value Problems by Viorel Barbu |
| title_full_unstemmed | Partial Differential Equations and Boundary Value Problems by Viorel Barbu |
| title_short | Partial Differential Equations and Boundary Value Problems |
| title_sort | partial differential equations and boundary value problems |
| topic | Mathematics Differential equations, partial Potential theory (Mathematics) Mathematical optimization Partial Differential Equations Applications of Mathematics Potential Theory Calculus of Variations and Optimal Control; Optimization Mathematik Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd Parabolisches Randwertproblem (DE-588)4319434-5 gnd Randwertproblem (DE-588)4048395-2 gnd Wellengleichung (DE-588)4065315-8 gnd |
| topic_facet | Mathematics Differential equations, partial Potential theory (Mathematics) Mathematical optimization Partial Differential Equations Applications of Mathematics Potential Theory Calculus of Variations and Optimal Control; Optimization Mathematik Lineare partielle Differentialgleichung Elliptisches Randwertproblem Parabolisches Randwertproblem Randwertproblem Wellengleichung |
| url | https://doi.org/10.1007/978-94-015-9117-1 |
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