Optimal control of partial differential equations II : theory and applications : conference held at the Mathematisches Forschungsinstitut, Oberwolfbach, May 18-24, 1986

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. 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 probƯ 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 hydrodyƯ 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 conƯ strained and unconstrained control problems. Also, very complex problems arising in the theory of free boundary value problems are treated.]~inally, some contribuƯ 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 atƯ 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 Front Matter....Pages 1-7 On a Domain Optimization Problem in Hydromechanics....Pages 9-27 On a Certain Optimal Harvesting Problem with Continuous Age Structure....Pages 29-42 Continuous Media: Interpretation in Terms of Phase-Portrait Method for Dynamic Systems with Control....Pages 43-55 Optimal Periodic Control of Quasilinear Systems in Hilbert Spaces....Pages 57-66 On an Inverse Problem for a Nonlinear Heat Equation Connected with Continuous Casting of Steel....Pages 67-89 Convergence of Suboptimal Controls for Point Targets....Pages 91-107 On State Constrained Optimal Shape Design Problems....Pages 109-122 An Application of Quasi Newton Methods to Pseudoparabolic Optimal Control Problems....Pages 123-138 Asymptotic Stability of Solutions to a Two-Phase Stefan Problem with Nonlinear Boundary Condition of Signorini Type....Pages 139-159 On the Control of the Secondary Cooling in the Continuous Casting Process....Pages 161-177 Optimal Control of Two-Phase Stefan Problems — Numerical Solutions....Pages 179-206 Justification of Necessary Optimality Conditions for Certain Integral Functionals....Pages 207-218 Semidiscrete Finite Element Approximation of Parabolic Boundary Control Problems — Convergence of Switching Points....Pages 219-232 Back Matter....Pages 233-234