An Introduction to the Theory of Viscosity Solutions for First-Order Hamilton–Jacobi Equations and Applications
Identifieur interne : 000012 ( Main/Exploration ); précédent : 000011; suivant : 000013An Introduction to the Theory of Viscosity Solutions for First-Order Hamilton–Jacobi Equations and Applications
Auteurs : Guy Barles [France]Source :
- Lecture Notes in Mathematics [ 0075-8434 ] ; NaN.
Abstract
Abstract: In this course, we first present an elementary introduction to the concept of viscosity solutions for first-order Hamilton–Jacobi Equations: definition, stability and comparison results (in the continuous and discontinuous frameworks), boundary conditions in the viscosity sense, Perron’s method, Barron–Jensen solutions … etc. We use a running example on exit time control problems to illustrate the different notions and results. In a second part, we consider the large time behavior of periodic solutions of Hamilton–Jacobi Equations: we describe recents results obtained by using partial differential equations type arguments. This part is complementary of the course of H. Ishii which presents the dynamical system approach (“weak KAM approach”).
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DOI: 10.1007/978-3-642-36433-4_2
Affiliations:
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