Representation Formulas for Contact Type Hamilton-Jacobi Equations
نویسندگان
چکیده
We discuss various kinds of representation formulas for the viscosity solutions contact type Hamilton-Jacobi equations by using Herglotz’ variational principle.
منابع مشابه
Hamilton-Jacobi-Bellman Equations
This work treats Hamilton-Jacobi-Bellman equations. Their relation to several problems in mathematics is presented and an introduction to viscosity solutions is given. The work of several research articles is reviewed, including the Barles-Souganidis convergence argument and the inaugural papers on mean-field games. Original research on numerical methods for Hamilton-Jacobi-Bellman equations is...
متن کاملMixed Finite Element Methods for Hamilton-Jacobi-Bellman Type Equations
The numerical solution of Dirichlet's problem for a second order elliptic operator in divergence form with arbitrary nonlinearities in the rst and zero order terms is considered. The mixed nite element method is used. Existence and uniqueness of the approximation are proved and optimal error estimates in L are demonstrated for the relevant functions. Error estimates are also derived in L, 2 q +...
متن کاملHypercontractivity of Hamilton–jacobi Equations
– Following the equivalence between logarithmic Sobolev inequalities and hypercontractivity showed by L. Gross, we prove that logarithmic Sobolev inequalities are related similarly to hypercontractivity of solutions of Hamilton–Jacobi equations. By the infimum-convolution description of the Hamilton–Jacobi solutions, this approach provides a clear view of the connection between logarithmic Sobo...
متن کاملSchrödinger and Hamilton-jacobi Equations
Time-dependent Schrödinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be shown that there is one-to-one physical correspondence between basic solutions (represented always by one Hamiltonian eigenfunction only) and classical ones, as ...
متن کاملFractal Hamilton-Jacobi-KPZ equations
Nonlinear and nonlinear evolution equations of the form ut = Lu ± |∇u| q, where L is a pseudodifferential operator representing the infinitesimal generator of a Lévy stochastic process, have been derived as models for growing interfaces in the case when the continuous Brownian diffusion surface transport is augmented by a random hopping mechanism. The goal of this paper is to study properties o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Dynamics and Differential Equations
سال: 2021
ISSN: ['1040-7294', '1572-9222']
DOI: https://doi.org/10.1007/s10884-021-09960-w