28 citations · 39 across the 14 of their papers we have counts for
7 papers · 1 filter
Nonlinear semigroup approach to Hamilton-Jacobi equations -- A toy model
Liang Jin, Jun Yan, Kai Zhao
In this paper, we discuss the existence and multiplicity problem of viscosity solution to the Hamilton-Jacobi equation where is a closed ma…
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…
Multi-objective Herglotz' variational principle and cooperative Hamilton-Jacobi systems
Wei Cheng, Kai Zhao, Min Zhou
We study a multi-objective variational problem of Herglotz' type with cooperative linear coupling. We established the associated Euler-Lagrange equations and the characteristic sys…
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…
Representation formulas for contact type Hamilton-Jacobi equations
Jiahui Hong, Wei Cheng, Shengqing Hu +1
We discuss various kinds of representation formulas for the viscosity solutions of the contact type Hamilton-Jacobi equations by using the Herglotz' variational principle.
Vanishing contact structure problem and convergence of the viscosity solutions
Qinbo Chen, Wei Cheng, Hitoshi Ishii +1
This paper is devoted to study the vanishing contact structure problem which is a generalization of the vanishing discount problem. Let be a family of Hamiltonians of…