A basic guide to uniqueness problems for evolutionary differential equations:
This book is intended to be a short introduction to uniqueness questions for initial value problems. One often weakens the notion of a solution to include non-differentiable solutions. Such a solution is called a weak solution. It is easier to find a weak solution, but it is more difficult to establ...
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| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham, Switzerland
Birkhäuser
[2023]
|
| Schriftenreihe: | Compact textbooks in mathematics
|
| Schlagworte: | |
| Zusammenfassung: | This book is intended to be a short introduction to uniqueness questions for initial value problems. One often weakens the notion of a solution to include non-differentiable solutions. Such a solution is called a weak solution. It is easier to find a weak solution, but it is more difficult to establish its uniqueness. This book examines three very fundamental equations: ordinary differential equations, scalar conservation laws, and Hamilton-Jacobi equations. Starting from the standard Gronwall inequality, this book discusses less regular ordinary differential equations. It includes an introduction of advanced topics like the theory of maximal monotone operators as well as what is called DiPerna-Lions theory, which is still an active research area. For conservation laws, the uniqueness of entropy solution, a special (discontinuous) weak solution is explained. For Hamilton-Jacobi equations, several uniqueness results are established for a viscosity solution, a kind of a non-differentiable weak solution. The uniqueness of discontinuous viscosity solution is also discussed. A detailed proof is given for each uniqueness statement. |
| Beschreibung: | x, 155 Seiten Illustrationen 23.5 gr |
| ISBN: | 9783031347955 |
Internformat
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| 245 | 1 | 0 | |a A basic guide to uniqueness problems for evolutionary differential equations |c Mi-Ho Giga, Yoshikazu Giga |
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| 520 | |a This book is intended to be a short introduction to uniqueness questions for initial value problems. One often weakens the notion of a solution to include non-differentiable solutions. Such a solution is called a weak solution. It is easier to find a weak solution, but it is more difficult to establish its uniqueness. This book examines three very fundamental equations: ordinary differential equations, scalar conservation laws, and Hamilton-Jacobi equations. Starting from the standard Gronwall inequality, this book discusses less regular ordinary differential equations. It includes an introduction of advanced topics like the theory of maximal monotone operators as well as what is called DiPerna-Lions theory, which is still an active research area. For conservation laws, the uniqueness of entropy solution, a special (discontinuous) weak solution is explained. For Hamilton-Jacobi equations, several uniqueness results are established for a viscosity solution, a kind of a non-differentiable weak solution. The uniqueness of discontinuous viscosity solution is also discussed. A detailed proof is given for each uniqueness statement. | ||
| 653 | |a Hardcover, Softcover / Mathematik/Analysis | ||
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| isbn | 9783031347955 |
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| physical | x, 155 Seiten Illustrationen 23.5 gr |
| publishDate | 2023 |
| publishDateSearch | 2023 |
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| publisher | Birkhäuser |
| record_format | marc |
| series2 | Compact textbooks in mathematics |
| spelling | Giga, Mi-Ho Verfasser aut A basic guide to uniqueness problems for evolutionary differential equations Mi-Ho Giga, Yoshikazu Giga Cham, Switzerland Birkhäuser [2023] x, 155 Seiten Illustrationen 23.5 gr txt rdacontent n rdamedia nc rdacarrier Compact textbooks in mathematics This book is intended to be a short introduction to uniqueness questions for initial value problems. One often weakens the notion of a solution to include non-differentiable solutions. Such a solution is called a weak solution. It is easier to find a weak solution, but it is more difficult to establish its uniqueness. This book examines three very fundamental equations: ordinary differential equations, scalar conservation laws, and Hamilton-Jacobi equations. Starting from the standard Gronwall inequality, this book discusses less regular ordinary differential equations. It includes an introduction of advanced topics like the theory of maximal monotone operators as well as what is called DiPerna-Lions theory, which is still an active research area. For conservation laws, the uniqueness of entropy solution, a special (discontinuous) weak solution is explained. For Hamilton-Jacobi equations, several uniqueness results are established for a viscosity solution, a kind of a non-differentiable weak solution. The uniqueness of discontinuous viscosity solution is also discussed. A detailed proof is given for each uniqueness statement. Hardcover, Softcover / Mathematik/Analysis Giga, Yoshikazu 1955- Verfasser (DE-588)121691195 aut Erscheint auch als Online-Ausgabe 978-3-031-34796-2 |
| spellingShingle | Giga, Mi-Ho Giga, Yoshikazu 1955- A basic guide to uniqueness problems for evolutionary differential equations |
| title | A basic guide to uniqueness problems for evolutionary differential equations |
| title_auth | A basic guide to uniqueness problems for evolutionary differential equations |
| title_exact_search | A basic guide to uniqueness problems for evolutionary differential equations |
| title_exact_search_txtP | A basic guide to uniqueness problems for evolutionary differential equations |
| title_full | A basic guide to uniqueness problems for evolutionary differential equations Mi-Ho Giga, Yoshikazu Giga |
| title_fullStr | A basic guide to uniqueness problems for evolutionary differential equations Mi-Ho Giga, Yoshikazu Giga |
| title_full_unstemmed | A basic guide to uniqueness problems for evolutionary differential equations Mi-Ho Giga, Yoshikazu Giga |
| title_short | A basic guide to uniqueness problems for evolutionary differential equations |
| title_sort | a basic guide to uniqueness problems for evolutionary differential equations |
| work_keys_str_mv | AT gigamiho abasicguidetouniquenessproblemsforevolutionarydifferentialequations AT gigayoshikazu abasicguidetouniquenessproblemsforevolutionarydifferentialequations |