O ptimal control problems governed by partial differential equations with state constraints are considered. The state constraints are treated by two types of regularization techniques, namely the Lavrentiev type and the Moreau-Yosida type regularization. For the realization of the numerical solution, a multigrid method is applied to the regularized problems. The main purpose of this research is...

We study local well-posedness and orbital stability/instability of standing waves for a first order system associated with nonlinear Klein–Gordon equation on star graph. The proof the uses classical fixed point argument Hille–Yosida theorem. Stability relies linearization approach recent results NLS ?-interaction

The numerical investigation of a recent family of algebraic fractional-step methods (the so called Yosida methods) for the solution of the incompressible time-dependent Navier–Stokes equations is presented. A comparison with the Karniadakis–Israeli–Orszag method Karniadakis et al. (1991, J. Comput. Phys. 97, 414–443) is carried out. The high accuracy in time of these schemes well combines with ...

In this work, we study the existence of periodic solutions for partial neutral functional differential equation. We assume that the linear part is not necessarily densely defined and satisfies the Hille-Yosida condition. In the nonhomogeneous linear case, we prove that the existence of a bounded solution on R+ implies the existence of a periodic solution. In nonlinear case, we use the concept o...

We derive a-priori estimates on the length of the primal-dual path that results from a Moreau-Yosida approximation of the feasible set for state constrained optimal control problems. These bounds depend on the regularity of the state and the dimension of the problem. Comparison with numerical results indicates that these bounds are sharp and are attained for the case of a single active point. A...