Convergence/divergence phenomena in the vanishing discount limit of Hamilton-Jacobi equations
We study the asymptotic behavior of solutions of an equation of the form\begin
{equation}\label {abs}\tag {*} G\big (x, D_x u,\lambda u (x)\big)= c_0\qquad\hbox {in $ M …
{equation}\label {abs}\tag {*} G\big (x, D_x u,\lambda u (x)\big)= c_0\qquad\hbox {in $ M …
The selection problem for a new class of perturbations of Hamilton-Jacobi equations and its applications
Q Chen - arXiv preprint arXiv:2412.20958, 2024 - arxiv.org
This paper studies a perturbation problem given by the equation:\begin {equation*} H (x,
d_xu_\lambda,\lambda u_\lambda (x))+\lambda V (x,\lambda)= c\quad\text {in $ M $},\end …
d_xu_\lambda,\lambda u_\lambda (x))+\lambda V (x,\lambda)= c\quad\text {in $ M $},\end …
A nonlinear semigroup approach to Hamilton-Jacobi equations–revisited
Abstract We consider the Hamilton-Jacobi equation H (x, D u)+ λ (x) u= c, x∈ M, where M is
a connected, closed and smooth Riemannian manifold. The functions H (x, p) and λ (x) are …
a connected, closed and smooth Riemannian manifold. The functions H (x, p) and λ (x) are …
Nonlinear and degenerate discounted approximation in discrete weak KAM theory
P Ni, M Zavidovique - arXiv preprint arXiv:2403.04563, 2024 - arxiv.org
In this paper, we introduce a discrete version of the nonlinear implicit Lax-Oleinik operator.
We consider the associated vanishing discount problem with a non-degenerate condition …
We consider the associated vanishing discount problem with a non-degenerate condition …