We discuss a class of time-dependent Hamilton-Jacobi equations, where an unknown function of time is intended to keep the maximum of the solution to the constant value 0. Our main result is that the full problem has a unique viscosity solution, which is in fact classical. The motivation is a selection-mutation model which, in the limit of small diffusion, exhibits concentration on the zero leve...

We consider the following evolutionary Hamilton-Jacobi equation with initial condition: { ∂tu(x, t) +H(x, u(x, t), ∂xu(x, t)) = 0, u(x, 0) = φ(x). Under some assumptions on H(x, u, p) with respect to p and u, we provide a variational principle on the evolutionary Hamilton-Jacobi equation. By introducing an implicitly defined solution semigroup, we extend Fathi’s weak KAM theory to certain more ...

in this paper, free vibration of functionally graded rectangular simply supported thick plates based on two variable refined plate theory is presented. according to a power-law distribution, the mass density and elasticity modulus of the plate are considered to vary while poisson’s ratio is constant. in order to extract the five constitutive equations of motion, hamilton principle is employed. ...

This paper investigates the optimal mean-variance reinsurance-investment problem for an insurer with a common shock dependence under two kinds of popular premium principles: variance principle and expected value principle. We formulate optimization within game theoretic framework derive closed-form expressions equilibrium strategy function different principles by solving extended Hamilton-Jacob...

In this paper, we discuss some principles on the selection of the solutions of a special vectorial Hamilton-Jacobi system defined by (1.1) below. We first classify the equivalent solutions based on a wellknown construction and then discuss some selection principles using intuitive descriptions of coarseness or maximality of solutions. We also discuss a selection principle based on comparison of...

We consider the optimal control of stochastic delayed systems with jumps, in which both the state and controls can depend on the past history of the system, for a value function which depends on the initial path of the process. We derive the Hamilton-Jacobi-Bellman equation and the associated verification theorem and prove a necessary and a sufficient maximum principles for such problems. Expli...

This paper presents a uni­ ed critical-point theory in non-smooth, non-convex and dissipative Hamilton systems. The canonical dual/polar transformation methods and the associated bi-duality and triality theories proposed recently in non-convex variational problems are generalized into fully nonlinear dissipative dynamical systems governed by non-smooth constitutive laws and boundary conditions....

In this paper we consider a rather general optimal control problem involving ordinary differential equations with delayed arguments and a set of equality and inequality restrictions on stateand control va~iaMes. For this problem a maximum principle is given in pointwise form, using variational techniques. From this maximum principle necessary conditions are derived, as well as a Lagrange-like m...