Distributions and nonlinear partial differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1978
|
| Series: | Lecture notes in mathematics
684 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 146 S. graph. Darst. |
| ISBN: | 3540089519 0387089519 |
Staff View
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| 245 | 1 | 0 | |a Distributions and nonlinear partial differential equations |c Elemer E. Rosinger |
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Record in the Search Index
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| adam_text | CONTENT
Chapter 1. Associative, Commutative Algebras Containing the Distributions . . 3
§1. Nonlinear Problems 3
§2. Motivation of the Approach 5
§3. Distribution Multiplication 7
§4. Algebras of Sequences of Smooth Functions 9
§5. Simpler Diagrams of Inclusions 12
§6. Admissible Properties 13
§7. Regularizations and Algebras Containing the Distributions 14
§8. Properties of the Families of Algebras Containing D (Rn) 18
§9. Defining Nonlinear Partial Differential Operators on the Algebras . 22
§10. Maximality and Local Vanishing 23
§11. Stronger Conditions for Derivatives 28
§12. Appendix 29
Chapter 2. Dirac Algebras Containing the Distributions 33
§1. Introduction 33
§2. Classes of Singularities of Piece Wise Smooth Functions 33
§3. Compatible Ideals and Vector Subspaces of Sequences
of Smooth Functions 34
§4. Locally Vanishing Ideals of Sequences of Smooth Functions 39
§5. Local Classes and Compatibility 42
§6. Dirac Algebras 45
§7. Maximality 47
§8. Local Algebras 49
§9. Filter Algebras 52
§10. Regular Algebras 55
Chapter 3. Solutions of Nonlinear Partial Differential Equations
Application to Nonlinear Shock Waves 60
§1. Introduction 60
§2. Polynomial Nonlinear Partial Differential Operators and Solutions . 60
§3. Application to Nonlinear Shock Waves 65
§4. General Solution Scheme for Nonlinear Partial Differential Equations 66
Chapter 4. Quantum Particle Scattering in Potentials Positive Powers
of the Dirac S Distribution 70
§1. Introduction 70
§2. Wave Functions, Junction Relations 70
§3. Weak Solution 72
§4. Smooth Representations for 5 78
§5. Wave Function Solutions in the Algebras
Containing the Distributions 82
Chapter 5. Products with Dirac Distributions 85
§1. Introduction • • t 85
§2. The Dirac Ideal 1° 86
§3. Compatible Dirac Classes Tj- 86
§4. Products with Dirac Distributions 89
§5. Formulas in Quantum Mechanics 94
§6. A Property of the Derivative in the Algebras 97
§7. The Existence of the Sequences in Z 98
§8. Stronger Relations Containing Products with Dirac Distributions . . 105
X
Chapter 6. Linear Independent Families of Dirac Distributions 111
II. Introduction 111
§2. Compatible Algebras and Transformations 111
§3. Linear Independent Families of Dirac Distributions 113
§4. Generalized Dirac Elements 115
Chapter 7. Support, Local Properties 120
§1. Introduction 120
§2. The Extended Notion of Support 120
§3. Localization 124
§4. The Equivalence between S = 0 and supp S = 0 131
Chapter 8. Necessary Structure of the Distribution Multiplications 132
Si. Introduction 132
§2. Zero Sets and Families 132
§3. Zero Sets and Families at a Point 134
Reference 139
|
| any_adam_object | 1 |
| author | Rosinger, Elemer E. |
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| author_variant | e e r ee eer |
| building | Verbundindex |
| bvnumber | BV002255938 |
| callnumber-first | Q - Science |
| callnumber-label | QA3 |
| callnumber-raw | QA3 |
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| callnumber-subject | QA - Mathematics |
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| dewey-sort | 3515 3353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | Partielle Funktionalgleichung gnd |
| genre_facet | Partielle Funktionalgleichung |
| id | DE-604.BV002255938 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:42:52Z |
| institution | BVB |
| isbn | 3540089519 0387089519 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001482458 |
| oclc_num | 5336161 |
| open_access_boolean | |
| owner | DE-12 DE-91G DE-BY-TUM DE-384 DE-473 DE-BY-UBG DE-355 DE-BY-UBR DE-20 DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-83 DE-11 DE-188 |
| owner_facet | DE-12 DE-91G DE-BY-TUM DE-384 DE-473 DE-BY-UBG DE-355 DE-BY-UBR DE-20 DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-83 DE-11 DE-188 |
| physical | XI, 146 S. graph. Darst. |
| publishDate | 1978 |
| publishDateSearch | 1978 |
| publishDateSort | 1978 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Rosinger, Elemer E. Verfasser aut Distributions and nonlinear partial differential equations Elemer E. Rosinger Berlin [u.a.] Springer 1978 XI, 146 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 684 Distribution (Théorie des probabilités) Équations aux dérivées partielles Équations différentielles non linéaires Differential equations, Partial Theory of distributions (Functional analysis) Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Theorie (DE-588)4059787-8 gnd rswk-swf Distribution Funktionalanalysis (DE-588)4070505-5 gnd rswk-swf Distributionstheorie (DE-588)4150254-1 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Partielle Funktionalgleichung gnd rswk-swf Distribution Funktionalanalysis (DE-588)4070505-5 s Partielle Funktionalgleichung f DE-604 Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s Partielle Differentialgleichung (DE-588)4044779-0 s Distributionstheorie (DE-588)4150254-1 s Theorie (DE-588)4059787-8 s Lecture notes in mathematics 684 (DE-604)BV000676446 684 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001482458&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rosinger, Elemer E. Distributions and nonlinear partial differential equations Lecture notes in mathematics Distribution (Théorie des probabilités) Équations aux dérivées partielles Équations différentielles non linéaires Differential equations, Partial Theory of distributions (Functional analysis) Partielle Differentialgleichung (DE-588)4044779-0 gnd Theorie (DE-588)4059787-8 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd Distributionstheorie (DE-588)4150254-1 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4059787-8 (DE-588)4070505-5 (DE-588)4150254-1 (DE-588)4128900-6 |
| title | Distributions and nonlinear partial differential equations |
| title_auth | Distributions and nonlinear partial differential equations |
| title_exact_search | Distributions and nonlinear partial differential equations |
| title_full | Distributions and nonlinear partial differential equations Elemer E. Rosinger |
| title_fullStr | Distributions and nonlinear partial differential equations Elemer E. Rosinger |
| title_full_unstemmed | Distributions and nonlinear partial differential equations Elemer E. Rosinger |
| title_short | Distributions and nonlinear partial differential equations |
| title_sort | distributions and nonlinear partial differential equations |
| topic | Distribution (Théorie des probabilités) Équations aux dérivées partielles Équations différentielles non linéaires Differential equations, Partial Theory of distributions (Functional analysis) Partielle Differentialgleichung (DE-588)4044779-0 gnd Theorie (DE-588)4059787-8 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd Distributionstheorie (DE-588)4150254-1 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| topic_facet | Distribution (Théorie des probabilités) Équations aux dérivées partielles Équations différentielles non linéaires Differential equations, Partial Theory of distributions (Functional analysis) Partielle Differentialgleichung Theorie Distribution Funktionalanalysis Distributionstheorie Nichtlineare partielle Differentialgleichung Partielle Funktionalgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001482458&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT rosingerelemere distributionsandnonlinearpartialdifferentialequations |