The classical form of Hamilton’s principle holds for conservative systems with perfect bilateral constraints. Several attempts have been made in literature to generalise Hamilton’s principle for mechanical systems with perfect unilateral constraints involving impulsive motion. This has led to a number of different variants of Hamilton’s principle, some expressed as variational inequalities. Up ...

this paper presents a mathematical model for the vibration analysis of a three-component piezoelectric force sensor. the cubic theory of weakly nonlinear electroelasticity is applied to the model for describing the electromechanical coupling effect in the piezoelectric sensing elements which operate in thickness-shear and thickness-stretch vibration modes. hamilton's principle is used to d...

We discuss various kinds of representation formulas for the viscosity solutions contact type Hamilton-Jacobi equations by using Herglotz’ variational principle.

The course deals with the analysis of optimal control problems and of the related first order PDEs of dynamic programming. In particular, we shall focus our attention on time optimal control problems for linear and nonlinear systems. We shall present some recent results concerning the regularity and the compactness of viscosity solutions to Hamilton-Jacobi and Hamilton-Jacobi-Bellmann Equations...

Large deviation for Markov processes can be studied by Hamilton– Jacobi equation techniques. The method of proof involves three steps: First, we apply a nonlinear transform to generators of the Markov processes, and verify that limit of the transformed generators exists. Such limit induces a Hamilton–Jacobi equation. Second, we show that a strong form of uniqueness (the comparison principle) ho...

Abstract We study the well-posedness of Hamilton–Jacobi–Bellman equations on subsets $${\mathbb {R}}^d$$ R d in a context without boundary conditions. The Hamiltonian is given as supremum over two parts: an internal depending external control vari...

Large deviation for Markov processes can be studied by Hamilton– Jacobi equation techniques. The method of proof involves three steps: First, we apply a nonlinear transform to generators of the Markov processes, and verify that limit of the transformed generators exists. Such limit induces a Hamilton–Jacobi equation. Second, we show that a strong form of uniqueness (the comparison principle) ho...

We show a comparison principle for viscosity superand subsolutions to Hamilton-Jacobi equations with discontinuous Hamiltonians. The key point is that the Hamiltonian depends upon u and has a special structure. The supersolution must enjoy some additional regularity.