Guy Barles's Books

On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities

A Guide to Theory, Applications, and Some Open Problems

By: Guy Barles,Emmanuel Chasseigne

Write a review Read reviews Take a Quiz Solve Book Puzzle

On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities

A Guide to Theory, Applications, and Some Open Problems

By: Guy Barles,Emmanuel Chasseigne

This monograph presents the most recent developments in the study of Hamilton-Jacobi Equations and control problems with discontinuities, mainly from the viewpoint of partial differential equations. Two main cases are investigated in detail: the case of codimension 1 discontinuities and the stratified case in which the discontinuities can be of any codimensions. In both, connections with deterministic control problems are carefully studied, and numerous examples and applications are illustrated throughout the text. After an initial section that provides a “toolbox” containing key results which will be used throughout the text, Parts II and III completely describe several recently introduced approaches to treat problems involving either codimension 1 discontinuities or networks. The remaining sections are concerned with stratified problems either in the whole space R^N or in bounded or unbounded domains with state-constraints. In particular, the use of stratified solutions to treat problems with boundary conditions, where both the boundary may be non-smooth and the data may present discontinuities, is developed. Many applications to concrete problems are explored throughout the text – such as Kolmogorov-Petrovsky-Piskunov (KPP) type problems, large deviations, level-sets approach, large time behavior, and homogenization – and several key open problems are presented. This monograph will be of interest to graduate students and researchers working in deterministic control problems and Hamilton-Jacobi Equations, network problems, or scalar conservation laws.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

569

Publisher

Springer Nature

Published Date

ISBN 10

3031493710

ISBN 13

9783031493713

Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications

Cetraro, Italy 2011, Editors: Paola Loreti, Nicoletta Anna Tchou

By: Yves Achdou,Guy Barles,Hitoshi Ishii,Grigory L. Litvinov

Write a review Read reviews Take a Quiz Solve Book Puzzle

Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications

Cetraro, Italy 2011, Editors: Paola Loreti, Nicoletta Anna Tchou

By: Yves Achdou,Guy Barles,Hitoshi Ishii,Grigory L. Litvinov

These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These lecture notes contain four contributions by Yves Achdou (Finite Difference Methods for Mean Field Games), Guy Barles (An Introduction to the Theory of Viscosity Solutions for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations).

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

316

Publisher

Springer

Published Date

ISBN 10

3642364330

ISBN 13

9783642364334

On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities

A Guide to Theory, Applications, and Some Open Problems

By: Guy Barles,Emmanuel Chasseigne

Write a review Read reviews Take a Quiz Solve Book Puzzle

On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities

A Guide to Theory, Applications, and Some Open Problems

By: Guy Barles,Emmanuel Chasseigne

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

569

Publisher

Springer Nature

Published Date

ISBN 10

3031493710

ISBN 13

9783031493713

Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications

Cetraro, Italy 2011, Editors: Paola Loreti, Nicoletta Anna Tchou

By: Yves Achdou,Guy Barles,Hitoshi Ishii,Grigory L. Litvinov

Write a review Read reviews Take a Quiz Solve Book Puzzle

Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications

Cetraro, Italy 2011, Editors: Paola Loreti, Nicoletta Anna Tchou

By: Yves Achdou,Guy Barles,Hitoshi Ishii,Grigory L. Litvinov

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

316

Publisher

Springer

Published Date

ISBN 10

3642364330

ISBN 13

9783642364334

Book's by Guy Barles

On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities

On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities

Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications

Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications

On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities

On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities

Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications

Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications

Username

Password

Username

Password

Password again

Birthday

Email