Solution of continuous nonlinear PDEs through order completion:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam u.a.
North-Holland
1994
|
| Series: | North-Holland mathematics studies
181 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 432 S. |
| ISBN: | 0444820353 |
Staff View
MARC
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| 245 | 1 | 0 | |a Solution of continuous nonlinear PDEs through order completion |c Michael B. Oberguggenberger ; Elemér E. Rosinger |
| 264 | 1 | |a Amsterdam u.a. |b North-Holland |c 1994 | |
| 300 | |a XVI, 432 S. | ||
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| 650 | 4 | |a Differential equations, Nonlinear |x Numerical solutions | |
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| adam_text | XIII
TABLE OF CONTENTS
PART I GENERAL EXISTENCE OF SOLUTIONS THEORY 1
Section 1 Introduction 3
Section 2 Approximation of Solutions of Continuous Nonlinear PDEs 11
Section 3 Spaces of Generalized Functions 24
Section 4 Extending T(x,D) to the Order Completion of
Spaces of Smooth Functions 31
Section 5 Existence of Generalized Solutions 38
Section 6 A Few First Examples 65
Section 7 Generalized Solutions as Measurable Functions 74
7.1 if0(n) and the Measurable Functions 74
7.2 The Flabby Sheaf Structure of ^((1)* 94
7.3 Further Examples and Counterexamples 146
PART II APPLICATIONS TO SPECIFIC CLASSES OF LINEAR AND
NONLINEAR PDEs 159
Section 8 The Cauchy Problem for Nonlinear First Order
Systems 161
Section 9 An Abstract Existence Result 184
Section 10 PDEs with Sufficiently Many Smooth Solutions 195
XIV
Section 11 Nonlinear Systems with Measures as Initial Data 210
11.1 Extension of an Existence Result 210
11.2 The Meaning of Generalized Solutions 225
Section 12 Solution of PDEs and the Completion of Uniform
Spaces 237
Section 13 Partial Orders Compatible with a Nonlinear
Partial Differential Operator 263
Section 14 Miscellaneous Results 278
14.1 Preliminaries 278
14.2 Simultaneous Solvability of a Family of
Nonlinear PDEs 278
14.3 Strengthened Approximation and Existence Results
with Conditions on Derivatives 288
PART III GROUP INVARIANCE OF GLOBAL GENERALIZED SOLUTIONS
OF NONLINEAR PDEs 295
Section 15 Introduction 297
Section 16 Group Invariance of Global Generalized Solutions
of Nonlinear PDEs Obtained Through the Algebraic
Method 299
16.0 Preliminaries 299
16.1 Hilbert s Fifth Problem 299
16.2 Review of the Global Existence Result 306
XV
16.3 Group Transformations for Functions 313
16.4 Group Transformations for Algebras of
Generalized Functions 315
16.5 Group Invariance for Global Generalized
Solutions 319
16.6 Computing Symmetry Groups for Global Generalized
Solutions 321
16.7 Application to Delta Waves of Semilinear
Hyperbolic PDEs 325
16.8 Application to Shock Vaves 331
16.9 The Case of Local Groups of Transformations 340
16.10 Local Group Invariance 344
Section 17 Group Invariance of Generalized Solutions
Obtained Through the Algebraic Method : An
Alternative Approach 354
17.0 Preliminaries 354
17.1 A Brief Review of the Structure of Colombeau s
Generalized Functions 355
17.2 Group Transformations on g(^) 359
17.3 Group Invariance of Global Generalized
Solutions 361
17.4 Symmetry Groups for Generalized Solutions 363
XVI
Section 18 Group Invariance of Global Generalized Solutions
Obtained Through the Order Completion Method 365
18.1 Introduction 365
18.2 Group Transformations of Spaces of Generalized
Functions 366
18.3 Group Transformations of Dedekind Order
Completions 375
18.4 Group Invariance of Global Generalized
Solutions 379
18.5 Computing Symmetry Groups for Global
Generalized Solutions 379
18.6 Application to Delta Vaves, Klein Gordon Equations
and Shock Waves 383
Appendix 389
References 421
Index 429
|
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| id | DE-604.BV009789562 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:40:54Z |
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| isbn | 0444820353 |
| language | English |
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| physical | XVI, 432 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | North-Holland |
| record_format | marc |
| series | North-Holland mathematics studies |
| series2 | North-Holland mathematics studies |
| spelling | Oberguggenberger, Michael 1953- Verfasser (DE-588)131514938 aut Solution of continuous nonlinear PDEs through order completion Michael B. Oberguggenberger ; Elemér E. Rosinger Amsterdam u.a. North-Holland 1994 XVI, 432 S. txt rdacontent n rdamedia nc rdacarrier North-Holland mathematics studies 181 Equations différentielles non linéaires - Solutions numériques ram Niet-lineaire vergelijkingen gtt Partiële differentiaalvergelijkingen gtt Differential equations, Nonlinear Numerical solutions Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s DE-604 Rosinger, Elemer E. Verfasser aut North-Holland mathematics studies 181 (DE-604)BV000003247 181 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006476796&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Oberguggenberger, Michael 1953- Rosinger, Elemer E. Solution of continuous nonlinear PDEs through order completion North-Holland mathematics studies Equations différentielles non linéaires - Solutions numériques ram Niet-lineaire vergelijkingen gtt Partiële differentiaalvergelijkingen gtt Differential equations, Nonlinear Numerical solutions Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| subject_GND | (DE-588)4128900-6 |
| title | Solution of continuous nonlinear PDEs through order completion |
| title_auth | Solution of continuous nonlinear PDEs through order completion |
| title_exact_search | Solution of continuous nonlinear PDEs through order completion |
| title_full | Solution of continuous nonlinear PDEs through order completion Michael B. Oberguggenberger ; Elemér E. Rosinger |
| title_fullStr | Solution of continuous nonlinear PDEs through order completion Michael B. Oberguggenberger ; Elemér E. Rosinger |
| title_full_unstemmed | Solution of continuous nonlinear PDEs through order completion Michael B. Oberguggenberger ; Elemér E. Rosinger |
| title_short | Solution of continuous nonlinear PDEs through order completion |
| title_sort | solution of continuous nonlinear pdes through order completion |
| topic | Equations différentielles non linéaires - Solutions numériques ram Niet-lineaire vergelijkingen gtt Partiële differentiaalvergelijkingen gtt Differential equations, Nonlinear Numerical solutions Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| topic_facet | Equations différentielles non linéaires - Solutions numériques Niet-lineaire vergelijkingen Partiële differentiaalvergelijkingen Differential equations, Nonlinear Numerical solutions Nichtlineare partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006476796&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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