Viscosity approximation of common fixed points for -Lipschitzian semigroup of pseudocontractive mappings in Banach spaces.
Viscosity approximation to common fixed points of families of nonexpansive mappings with weakly contractive mappings.
Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities
We study a finite horizon problem for a system whose evolution is governed by a controlled ordinary differential equation, which takes also account of a hysteretic component: namely, the output of a Preisach operator of hysteresis. We derive a discontinuous infinite dimensional Hamilton–Jacobi equation and prove that, under fairly general hypotheses, the value function is the unique bounded and uniformly continuous viscosity solution of the corresponding Cauchy problem.
Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities
We study a finite horizon problem for a system whose evolution is governed by a controlled ordinary differential equation, which takes also account of a hysteretic component: namely, the output of a Preisach operator of hysteresis. We derive a discontinuous infinite dimensional Hamilton–Jacobi equation and prove that, under fairly general hypotheses, the value function is the unique bounded and uniformly continuous viscosity solution of the corresponding Cauchy problem.