Generalized solutions of nonlinear partial differential equations
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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c1987
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| Schriftenreihe: | North-Holland mathematics studies
146 Notas de matemática (Rio de Janeiro, Brazil) no. 119 |
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| 500 | |a During the last few years, several fairly systematic nonlinear theories of generalized solutions of rather arbitrary nonlinear partial differential equations have emerged. The aim of this volume is to offer the reader a sufficiently detailed introduction to two of these recent nonlinear theories which have so far contributed most to the study of generalized solutions of nonlinear partial differential equations, bringing the reader to the level of ongoing research. The essence of the two nonlinear theories presented in this volume is the observation that much of the mathematics concerning existence, uniqueness regularity, etc., of generalized solutions for nonlinear partial differential equations can be reduced to elementary calculus in Euclidean spaces, combined with elementary algebra in quotient rings of families of smooth functions on Euclidean spaces, all of that joined by certain asymptotic interpretations. | ||
| 500 | |a In this way, one avoids the complexities and difficulties of the customary functional analytic methods which would involve sophisticated topologies on various function spaces. The result is a rather elementary yet powerful and far-reaching method which can, among others, give generalized solutions to linear and nonlinear partial differential equations previously unsolved or even unsolvable within distributions or hyperfunctions. Part 1 of the volume discusses the basic limitations of the linear theory of distributions when dealing with linear or nonlinear partial differential equations, particularly the impossibility and degeneracy results. Part 2 examines the way Colombeau constructs a nonlinear theory of generalized functions and then succeeds in proving quite impressive existence, uniqueness, regularity, etc., results concerning generalized solutions of large classes of linear and nonlinear partial differential equations. | ||
| 500 | |a Finally, Part 3 is a short presentation of the nonlinear theory of Rosinger, showing its connections with Colombeau's theory, which it contains as a particular case | ||
| 500 | |a Includes bibliographical references (p. 403-409) | ||
| 650 | 4 | |a Équations aux dérivées partielles / Solutions numériques | |
| 650 | 4 | |a Équations différentielles non linéaires / Solutions numériques | |
| 650 | 7 | |a Differential equations, Nonlinear / Numerical solutions |2 fast | |
| 650 | 7 | |a Differential equations, Partial / Numerical solutions |2 fast | |
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Datensatz im Suchindex
| _version_ | 1819294036074168320 |
|---|---|
| any_adam_object | |
| author | Rosinger, Elemer E. |
| author_facet | Rosinger, Elemer E. |
| author_role | aut |
| author_sort | Rosinger, Elemer E. |
| author_variant | e e r ee eer |
| building | Verbundindex |
| bvnumber | BV042317759 |
| collection | ZDB-33-ESD ZDB-33-EBS |
| ctrlnum | (ZDB-33-EBS)ocn316568554 (OCoLC)316568554 (DE-599)BVBBV042317759 |
| dewey-full | 510 515.3/55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 515 - Analysis |
| dewey-raw | 510 515.3/55 |
| dewey-search | 510 515.3/55 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-12-24T04:19:56Z |
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| isbn | 9780444703101 0444703101 9780080872575 0080872573 1281793078 9781281793072 |
| language | English |
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| physical | 1 Online-Ressource (xvii, 409 p.) |
| psigel | ZDB-33-ESD ZDB-33-EBS FAW_PDA_ESD FLA_PDA_ESD |
| publishDate | 1987 |
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| publisher | North-Holland |
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| series2 | North-Holland mathematics studies Notas de matemática (Rio de Janeiro, Brazil) |
| spelling | Rosinger, Elemer E. Verfasser aut Generalized solutions of nonlinear partial differential equations Elemér E. Rosinger Amsterdam North-Holland c1987 1 Online-Ressource (xvii, 409 p.) txt rdacontent c rdamedia cr rdacarrier North-Holland mathematics studies 146 Notas de matemática (Rio de Janeiro, Brazil) no. 119 During the last few years, several fairly systematic nonlinear theories of generalized solutions of rather arbitrary nonlinear partial differential equations have emerged. The aim of this volume is to offer the reader a sufficiently detailed introduction to two of these recent nonlinear theories which have so far contributed most to the study of generalized solutions of nonlinear partial differential equations, bringing the reader to the level of ongoing research. The essence of the two nonlinear theories presented in this volume is the observation that much of the mathematics concerning existence, uniqueness regularity, etc., of generalized solutions for nonlinear partial differential equations can be reduced to elementary calculus in Euclidean spaces, combined with elementary algebra in quotient rings of families of smooth functions on Euclidean spaces, all of that joined by certain asymptotic interpretations. In this way, one avoids the complexities and difficulties of the customary functional analytic methods which would involve sophisticated topologies on various function spaces. The result is a rather elementary yet powerful and far-reaching method which can, among others, give generalized solutions to linear and nonlinear partial differential equations previously unsolved or even unsolvable within distributions or hyperfunctions. Part 1 of the volume discusses the basic limitations of the linear theory of distributions when dealing with linear or nonlinear partial differential equations, particularly the impossibility and degeneracy results. Part 2 examines the way Colombeau constructs a nonlinear theory of generalized functions and then succeeds in proving quite impressive existence, uniqueness, regularity, etc., results concerning generalized solutions of large classes of linear and nonlinear partial differential equations. Finally, Part 3 is a short presentation of the nonlinear theory of Rosinger, showing its connections with Colombeau's theory, which it contains as a particular case Includes bibliographical references (p. 403-409) Équations aux dérivées partielles / Solutions numériques Équations différentielles non linéaires / Solutions numériques Differential equations, Nonlinear / Numerical solutions fast Differential equations, Partial / Numerical solutions fast MATHEMATICS / Differential Equations / General bisacsh Differential equations, Partial Numerical solutions Differential equations, Nonlinear Numerical solutions Schwache Lösung (DE-588)4131068-8 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s Numerisches Verfahren (DE-588)4128130-5 s 1\p DE-604 Schwache Lösung (DE-588)4131068-8 s 2\p DE-604 Numerische Mathematik (DE-588)4042805-9 s 3\p DE-604 http://www.sciencedirect.com/science/book/9780444703101 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 |
| spellingShingle | Rosinger, Elemer E. Generalized solutions of nonlinear partial differential equations Équations aux dérivées partielles / Solutions numériques Équations différentielles non linéaires / Solutions numériques Differential equations, Nonlinear / Numerical solutions fast Differential equations, Partial / Numerical solutions fast MATHEMATICS / Differential Equations / General bisacsh Differential equations, Partial Numerical solutions Differential equations, Nonlinear Numerical solutions Schwache Lösung (DE-588)4131068-8 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Numerische Mathematik (DE-588)4042805-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4131068-8 (DE-588)4128900-6 (DE-588)4042805-9 (DE-588)4128130-5 |
| title | Generalized solutions of nonlinear partial differential equations |
| title_auth | Generalized solutions of nonlinear partial differential equations |
| title_exact_search | Generalized solutions of nonlinear partial differential equations |
| title_full | Generalized solutions of nonlinear partial differential equations Elemér E. Rosinger |
| title_fullStr | Generalized solutions of nonlinear partial differential equations Elemér E. Rosinger |
| title_full_unstemmed | Generalized solutions of nonlinear partial differential equations Elemér E. Rosinger |
| title_short | Generalized solutions of nonlinear partial differential equations |
| title_sort | generalized solutions of nonlinear partial differential equations |
| topic | Équations aux dérivées partielles / Solutions numériques Équations différentielles non linéaires / Solutions numériques Differential equations, Nonlinear / Numerical solutions fast Differential equations, Partial / Numerical solutions fast MATHEMATICS / Differential Equations / General bisacsh Differential equations, Partial Numerical solutions Differential equations, Nonlinear Numerical solutions Schwache Lösung (DE-588)4131068-8 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Numerische Mathematik (DE-588)4042805-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Équations aux dérivées partielles / Solutions numériques Équations différentielles non linéaires / Solutions numériques Differential equations, Nonlinear / Numerical solutions Differential equations, Partial / Numerical solutions MATHEMATICS / Differential Equations / General Differential equations, Partial Numerical solutions Differential equations, Nonlinear Numerical solutions Schwache Lösung Nichtlineare partielle Differentialgleichung Numerische Mathematik Numerisches Verfahren |
| url | http://www.sciencedirect.com/science/book/9780444703101 |
| work_keys_str_mv | AT rosingerelemere generalizedsolutionsofnonlinearpartialdifferentialequations |