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Optimal damping control and nonlinear elliptic systems. (English) Zbl 0742.49017

The paper discusses an optimal control problem for a linear elliptic equation with zero-order coefficient as control and quadratic cost functional. Under some assumption (3.1) (which guarantees that the first and second derivatives of the state with respect to the control are small) it is shown that an iterative procedure (based on necessary conditions for optimality) converges to the solution of the problem. A numerical example is presented which shows that the given procedure works for cases where the condition (3.1) is not satisfied.
Reviewer: U.Raitums (Riga)

MSC:

49K20 Optimality conditions for problems involving partial differential equations
35J60 Nonlinear elliptic equations
49M05 Numerical methods based on necessary conditions
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