On pseudoparabolic optimal control problems. (English) Zbl 0810.49005

This paper discusses the following optimal control problem \[ J(u)= \min_{u\in U_{ad}} J(u)= \min_{u\in U_{ad}} \{\| Dy(T,u)- z_ d\|^ 2_ X+ j(u)\}, \] subject to the pseudoparabolic equations \[ A_ 1(t,u) y_ t(t,u)+ A_ 0(t,u) y(t,u)= f(t),\;A_ 1(0,u) y_ t(0,u)= f_ 0, \] where \(A_ 1(\cdot,\cdot)\), \(A_ 0(\cdot,\cdot)\), \(f(\cdot)\), \(j(\cdot)\) satisfy certain conditions. An existence theorem, conditions for the uniqueness and sensitivity analysis are presented.


49J20 Existence theories for optimal control problems involving partial differential equations
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