Dynamics of globally minimizing orbits in contact Hamiltonian systems
Y Xu, J Yan, K Zhao - arXiv preprint arXiv:2412.20658, 2024 - arxiv.org
Dynamics of globally minimizing orbits in contact Hamiltonian systems arXiv:2412.20658v1 [math.DS]
30 Dec 2024 Page 1 Dynamics of globally minimizing orbits in contact Hamiltonian systems …
30 Dec 2024 Page 1 Dynamics of globally minimizing orbits in contact Hamiltonian systems …
The asymptotic problem on contact Hamilton–Jacobi equations with state constraints
X Hu - Communications in Nonlinear Science and Numerical …, 2025 - Elsevier
We investigate the long time behavior of the viscosity solution for the evolutionary contact
Hamilton–Jacobi equation with state constraints. Our analysis reveals that the viscosity …
Hamilton–Jacobi equation with state constraints. Our analysis reveals that the viscosity …
A representation formula of the viscosity solution of the contact Hamilton-Jacobi equation and its applications
Assume $ M $ is a closed, connected and smooth Riemannian manifold. We consider the
evolutionary Hamilton-Jacobi equation\begin {equation*}\left\{\begin {aligned} &\partial_t u …
evolutionary Hamilton-Jacobi equation\begin {equation*}\left\{\begin {aligned} &\partial_t u …
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 …
Stability of solutions to contact Hamilton-Jacobi equation on the circle
Y Xu, J Yan, K Zhao - arXiv preprint arXiv:2401.14679, 2024 - arxiv.org
Combing the weak KAM method for contact Hamiltonian systems and the theory of viscosity
solutions for Hamilton-Jacobi equations, we study the Lyapunov stability and instability of …
solutions for Hamilton-Jacobi equations, we study the Lyapunov stability and instability of …
Rate of convergence for homogenization of nonlinear weakly coupled Hamilton-Jacobi systems
H Mitake, P Ni - arXiv preprint arXiv:2412.06428, 2024 - arxiv.org
arXiv:2412.06428v1 [math.AP] 9 Dec 2024 Page 1 arXiv:2412.06428v1 [math.AP] 9 Dec 2024
RATE OF CONVERGENCE FOR HOMOGENIZATION OF NONLINEAR WEAKLY COUPLED …
RATE OF CONVERGENCE FOR HOMOGENIZATION OF NONLINEAR WEAKLY COUPLED …
Lower gradient estimates for viscosity solutions to first-order Hamilton--Jacobi equations depending on the unknown function
K Hirose - arXiv preprint arXiv:2407.04288, 2024 - arxiv.org
In this paper, we derive the lower bounds for the gradients of viscosity solutions to the
Hamilton--Jacobi equation, where the convex Hamiltonian depends on the unknown …
Hamilton--Jacobi equation, where the convex Hamiltonian depends on the unknown …
Stability and weak KAM solutions of contact Hamilton-Jacobi equation
Y Xu, J Yan, K Zhao - Proceedings of the American Mathematical Society, 2024 - ams.org
We are concerned with the stability of viscosity solutions to contact Hamilton-Jacobi
equation\begin {align*} H (x,\partial _x u (x), u (x))= 0,\quad x\in M,\end {align*} where $ H …
equation\begin {align*} H (x,\partial _x u (x), u (x))= 0,\quad x\in M,\end {align*} where $ H …
Weakly coupled Hamilton-Jacobi systems without monotonicity condition: A first step
P Ni - arXiv preprint arXiv:2112.04885, 2021 - arxiv.org
In this paper, we mainly focus on the existence of the viscosity solutions of stationary weakly
coupled Hamilton-Jacobi systems\begin {equation*}\left\{\begin {aligned} &H_1 (x, Du_1 (x) …
coupled Hamilton-Jacobi systems\begin {equation*}\left\{\begin {aligned} &H_1 (x, Du_1 (x) …