32 citations · 71 across the 18 of their papers we have counts for
18 papers
Generalized Hamiltonian gradient flow of contact type I: regularity of the fundamental solutions
Wei Cheng, Shengqing Hu, Kaizhi Wang
This paper studies generalized Hamiltonian gradient flows for contact-type Hamilton--Jacobi equations, adopting the variational framework of Herglotz's principle and its fundamenta…
Lyapunov stability and uniqueness problems for Hamilton-Jacobi equations without monotonicity
Yuqi Ruan, Kaizhi Wang, Jun Yan
We consider the evolutionary Hamilton-Jacobi equation \begin{align*} w_t(x,t)+H(x,Dw(x,t),w(x,t))=0, \quad(x,t)\in M\times [0,+\infty), \end{align*} where is a compact manifold…
Variational construction of singular characteristics and propagation of singularities
Piermarco Cannarsa, Wei Cheng, Jiahui Hong +1
On a smooth closed manifold , we introduce a novel theory of maximal slope curves for any pair with a semiconcave function and a Hamiltonian. By using the notion…
Time periodic and almost periodic viscosity solutions of contact Hamilton-Jacobi equations on
Kaizhi Wang, Jun Yan, Kai Zhao
This paper concerns with the time periodic viscosity solution problem for a class of evolutionary contact Hamilton-Jacobi equations with time independent Hamiltonians on the torus…
Time-periodic solutions of contact Hamilton-Jacobi equations on the circle
Kaizhi Wang, Jun Yan, Kai Zhao
We are concerned with the existence and multiplicity of nontrivial time-periodic viscosity solutions to \[ \partial_t w(x,t) + H( x,\partial_x w(x,t),w(x,t) )=0,\quad (x,t)\in \mat…
Hamilton-Jacobi equations with their Hamiltonians depending Lipschitz continuously on the unknown
Hitoshi Ishii, Kaizhi Wang, Lin Wang +1
We study the Hamilton-Jacobi equations in and in , where the Hamiltonian depends Lipschitz…
Aubry-Mather theory for contact Hamiltonian systems II
Kaizhi Wang, Lin Wang, Jun Yan
In this paper, we continue to develop Aubry-Mather and weak KAM theories for contact Hamiltonian systems with certain dependence on the contact variable . For the Lip…
Ergodic problems for contact Hamilton-Jacobi equations
Kaizhi Wang, Jun Yan
This paper deals with the generalized ergodic problem \[ H(x,u(x),Du(x))=c, \quad x\in M, \] where the unknown is a pair of a constant and a function …
Finite-time convergence of solutions of Hamilton-Jacobi equations
Kaizhi Wang, Jun Yan, Kai Zhao
Suppose that is strictly decreasing in and satisfies Tonelli conditions in . We show that each viscosity solution of can be reached by many viscosi…
Herglotz' variational principle and Lax-Oleinik evolution
Piermarco Cannarsa, Wei Cheng, Liang Jin +2
We develop an elementary method to give a Lipschitz estimate for the minimizers in the problem of Herglotz' variational principle proposed in \cite{CCWY2018} in the time-dependent…
Long Time Behavior of First Order Mean Field Games on Euclidean Space
Piermarco Cannarsa, Wei Cheng, Cristian Mendico +1
The aim of this paper is to study the long time behavior of solutions to deterministic mean field games systems on Euclidean space. This problem was addressed on the torus ${\mathb…
Weak KAM solutions of Hamilton-Jacobi equations with decreasing dependence on unknown functions
Kaizhi Wang, Lin Wang, Jun Yan
We consider the Hamilton-Jacobi equation \[{H}(x,u,Du)=0,\quad x\in M, \] where is a connected, closed and smooth Riemannian manifold, satisfies Tonelli conditions…
Herglotz' generalized variational principle and contact type Hamilton-Jacobi equations
Piermarco Cannarsa, Wei Cheng, Kaizhi Wang +1
We develop an approach for the analysis of fundamental solutions to Hamilton-Jacobi equations of contact type based on a generalized variational principle proposed by Gustav Herglo…
Global generalized characteristics for the Dirichlet problem for Hamilton-Jacobi equations at a supercritical energy level
Piermarco Cannarsa, Wei Cheng, Marco Mazzola +1
We study the nonhomogeneous Dirichlet problem for first order Hamilton-Jacobi equations associated with Tonelli Hamiltonians on a bounded domain of assuming the energy l…
Aubry-Mather and weak KAM theories for contact Hamiltonian systems. Part 1: Strictly increasing case
Kaizhi Wang, Lin Wang, Jun Yan
This paper is concerned with the study of Aubry-Mather and weak KAM theories for contact Hamiltonian systems with Hamiltonians defined on , satisfy…
Variational principle for contact Hamiltonian systems and its applications
Kaizhi Wang, Lin Wang, Jun Yan
In \cite{WWY}, the authors provided an implicit variational principle for the contact Hamilton's equations \begin{align*} \left\{ \begin{array}{l} \dot{x}=\frac{\partial H}{\partia…
The rate of convergence of new Lax-Oleinik type operators for time-periodic positive definite Lagrangian systems
Kaizhi Wang, Jun Yan
Assume that the Aubry set of the time-periodic positive definite Lagrangian consists of one hyperbolic 1-periodic orbit. We provide an upper bound estimate of the rate of conve…
A new kind of Lax-Oleinik type operator with parameters for time-periodic positive definite Lagrangian systems
Kaizhi Wang, Jun Yan
In this paper we introduce a new kind of Lax-Oleinik type operator with parameters associated with positive definite Lagrangian systems for both the time-periodic case and the time…