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Optimal location of controllers for the one-dimensional wave equation
In this paper, we consider the homogeneous one-dimensional wave equation defined on (0,π). For every subset ωâŠ[0,π] of positive measure, every T≥2π, and all initial data, there exists a unique control of minimal norm in ...
The vanishing viscosity method for the sensitivity analysis of an optimal control problem of conservation laws in the presence of shocks
In this article we study, by the vanishing viscosity method, the sensitivity analysis of an optimal control problem for 1-D scalar conservation laws in the presence of shocks. It is reduced to investigate the vanishing ...
A penalization and regularization technique in shape optimization problems
We consider shape optimization problems, where the state is governed by elliptic partial differential equations. Using a regularization technique, unknown shapes are encoded via shape functions, turning the shape optimization ...