This book gives an extensive survey of many important topics in the theory of Hamilton-Jacobi equations with particular emphasis on modern approaches and viewpoints. Firstly, the basic well-posedness theory of viscosity solutions for first-order Hamilton-Jacobi equations is covered. Then, the homogenization theory, a very active research topic since the late 1980s but not covered in any standard textbook, is discussed in depth. Afterwards, dynamical properties of solutions, the Aubry-Mather theory, and weak Kolmogorov-Arnold-Moser (KAM) theory are studied. Both dynamical and PDE approaches are introduced to investigate these theories. Connections between homogenization, dynamical aspects, and the optimal rate of convergence in homogenization theory are given as well.
The book is self-contained and is useful for a course or for references. It can also serve as a gentle introductory reference to the homogenization theory.
| ISBN: | 9781470465551 |
| Publication date: | 30th January 2022 |
| Author: | Hung V Tran |
| Publisher: | American Mathematical Society |
| Format: | Paperback |
| Pagination: | 322 pages |
| Series: | Graduate Studies in Mathematics |
| Genres: |
Differential calculus and equations |
This book gives an extensive survey of many important topics in the theory of Hamilton-Jacobi equations with particular emphasis on modern approaches and viewpoints. Firstly, the basic well-posedness theory of viscosity solutions for first-order Hamilton-Jacobi equations is covered. Then, the homogenization theory, a very active research topic since the late 1980s but not covered in any standard textbook, is discussed in depth. Afterwards, dynamical properties of solutions, the Aubry-Mather theory, and weak Kolmogorov-Arnold-Moser (KAM) theory are studied. Both dynamical and PDE approaches are introduced to investigate these theories. Connections between homogenization, dynamical aspects, and the optimal rate of convergence in homogenization theory are given as well.
The book is self-contained and is useful for a course or for references. It can also serve as a gentle introductory reference to the homogenization theory.
Hamilton-Jacobi Equations features in the following genres: Differential calculus and equations
Hamilton-Jacobi Equations is available in Paperback, Hardback
Hamilton-Jacobi Equations was written by Hung V Tran and published by American Mathematical Society
Hamilton-Jacobi Equations has 322 pages
Yes it is part of Graduate Studies in Mathematics series