This volume contains the contributions of participants of the conference "Optimal Control of Partial Differential Equations" which, under the chairmanship of the editors, took place at the Mathematisches Forschungsinstitut Oberwolfach from May 18 to May 24, 1986. The great variety of topics covered by the contributions strongly indicates that also in the future it will be impossible to develop a unifying control theory of partial differential equations. On the other hand, there is a strong tendency to treat prob lems which are directly connected to practical applications. So this volume contains real-world applications like optimal cooling laws for the production of rolled steel or concrete solutions for the problem of optimal shape design in mechanics and hydrody namics. Another main topic is the construction of numerical methods. This includes applications of the finite element method as well as of Quasi-Newton-methods to con strained and unconstrained control problems. Also, very complex problems arising in the theory of free boundary value problems are treated. ]~inally, some contribu tions show how practical problems stimulate the further development of the theory; in particular, this is the case for fields like suboptimal control, necessary optimality conditions and sensitivity analysis. As usual, the lectures and stimulating discussions took place in the pleasant at mosphere of the Mathematisches Forschungsinstitut Oberwolfach. Special thanks of the participants are returned to the Director as well as to the staff of the institute.

Inhalt
On a Domain Optimization Problem in Hydromechanics.- On a Certain Optimal Harvesting Problem with Continuous Age Structure.- A Continuous Media: Interpretation Terms of Phase-Portrait Method for Dynamic Systems.- Optimal Periodic Control of Quasilinear Systems in Hilbert Spaces.- An Inverse Problem for a Nonlinear Heat Equation Connected with Continuous Casting of Steel.- Convergence of Suboptimal Controls for Point Targets.- On State Constrained Optimal Shape Design Problems.- An Application of Quasi Newton Methods to Pseudoparabolic Optimal Control Problems.- Asymptotic Stability of Solutions to a Two-Phase Stefan Problem with Nonlinear Boundary Condition of Signorini Type.- On the Control of the Secondary Cooling in the Continuous Casting Process.- Optimal Control of Two-Phase Stefan Problems Numerical Solutions.- Justification of Necessary Optimal Conditions for Certain Integral Functionals.- Semidiscrete Finite Element Approximation of Parabolic Boundary Control Problems Convergence of Switching Points.