On Existence and Uniqueness of Solutions of Hamilton-Jacobi Equations

Download or read book On Existence and Uniqueness of Solutions of Hamilton-Jacobi Equations written by M. G. Crandall and published by . This book was released on 1984 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of scalar first order nonlinear partial differential equations has been enjoying a rapid development in the last few years. This development occurred because the authors established uniqueness criteria for generalized solutions - called viscosity solutions - which correctly identify the solutions sought in areas of application, including control theory, differential games and the calculus of variations. The concept of viscosity solutions is relatively easy to work with and many formally heuristic or difficult proofs have been made rigorous or simple using this concept. A feedback process has begun and the experience recently gained in working with viscosity solution has suggested new existence and uniqueness results. The current paper continues this interaction by establishing new existence ane uniqueness results in a natural generality suggested by earlier proofs. It is also felt that the presentation of the comparison results, which imply uniqueness, continuous dependence, and are used to estimate moduli of continuity, has something to offer over earlier presentations in special cases.(Author).