On Eigenfunction Expansion of Solutions to the Hamilton Equations
نویسندگان
چکیده
منابع مشابه
On Viscosity Solutions of Hamilton-jacobi Equations
We consider the Dirichlet problem for Hamilton-Jacobi equations and prove existence, uniqueness and continuous dependence on boundary data of Lipschitz continuous maximal viscosity solutions.
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We consider here only the case where H = H(x, p) is a convex function with respect to the p variable. In this setting, representation formulas can be obtained by exploiting the well known connection existing via convex duality between the Hamilton Jacobi equation (1.1) with Calculus of Variations or, more generally, Optimal Control problems. In Section 1 we briefly review some known existence r...
متن کاملViscosity Solutions of Hamilton-Jacobi Equations
Problems involving Hamilton-Jacobi equations-which we take to be either of the stationary form H(x, u, Du) = 0 or of the evolution form u, + H(x, t, u, Du) = 0, where Du is the spatial gradient of u-arise in many contexts. Classical analysis of associated problems under boundary and/or initial conditions by the method of characteristics is limited to local considerations owing to the crossing o...
متن کاملGeometrical Solutions of Hamilton-jacobi Equations
The concept of the geometrical solution of Hamilton-Jacobi equations in arbitrary space dimension is introduced. The characterization of such solution is based on the intersection of several invariant hyper-surfaces in the space of 1-jets. This solution notion allows not only for the smooth evolution beyond the usual singularity formation but also for superposition of underlying geometrical sol...
متن کاملMetric Viscosity Solutions of Hamilton-jacobi Equations
A theory of viscosity solutions in metric spaces based on local slopes was initiated in [39]. In this manuscript we deepen the study of [39] and present a more complete account of the theory of metric viscosity solutions of Hamilton–Jacobi equations. Several comparison and existence results are proved and the main techniques for such metric viscosity solutions are illustrated.
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ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 2013
ISSN: 0022-4715,1572-9613
DOI: 10.1007/s10955-013-0846-1