Fractional order differentiability of the gradient of solutions to elliptic equations with mixed boundary conditions

SIGLEAvailable from TIB Hannover: RR 6329(96-22) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

On Maxwell's equations in exterior domains

In this paper the long time asymptotic behavior of solutions of Maxwell's equations with electric conductivity in an exterior domain with mixed boundary conditions is investigated. It is shown that the solution behaves asymptotically like a free space solution provided it obeys a suitable local decay-property. As a consequence the completeness of the wave-operators is obtained under very general assumptions on the coefficients. (orig.)Available from TIB Hannover: RR 6329(99-17) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Asymptotic behaviour of solutions of semilinear hyperbolic systems in arbitrary domains

In this paper the long time asymptotic behavior of solutions of semilinear symmetric hyperbolic system including Maxwell's equations and the scalar wave-equation in an arbitrary domain are investigated. The possibly nonlinear damping term may vanish on a certain subset of the domain. It is shown that the solution decays weakly to zero if and only if the initial-state is orthogonal to all stationary states. In the case that the nonlinear damping is in addition monotone, also strong local L"q-convergence is shown. (orig.)Available from TIB Hannover: RR 6329(98-25) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

A compactness result for vector fields with divergence and curl in L"q(#OMEGA#) involving mixed boundary conditions

It is shown that the space of all vector fields with divergence and curl in L"q(#OMEGA#), q#<=#2 such that the normal-component vanishes one part of #partial deriv##OMEGA# and the tangential-component vanishes on the other, is compactly imbedded in L"2(#OMEGA#). (orig.)SIGLEAvailable from TIB Hannover: RR 6329(97-10) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDeutsche Forschungsgemeinschaft (DFG), Bonn (Germany)DEGerman

Qualitative behavior of weak solutions of the drift diffusion model for semiconductor devices coupled with Maxwell's equations

The transient drift-diffusion model describing the charge transport in semiconductors is considered. Poisson's equation, which is usually used, is replaced by Maxwell's equations. The diffusion- and mobility-coefficients and the dielectric and magnetic susceptibilities may depend on the space-variables. Global existence and convergence to the thermal equilibrium is shown. (orig.)SIGLEAvailable from TIB Hannover: RR 6329(96-34) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDeutsche Forschungsgemeinschaft (DFG), Bonn (Germany)DEGerman

Strong convexity and directional derivates of marginal values in two-stage stochastic programming

Two-stage stochastic programs with random right-hand side are considered. Verifiable sufficient conditions for the existence of second-order directional derivatives of marginal values are presented. The central role of the strong convexity of the expected recourse function as well of a Lipschitz stability result for optimal sets is emphasized. (orig.)Available from TIB Hannover: RO 7722(484) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

On structure and stability in stochastic programs with random technology matrix and complete integer recourse

For two-stage stochastic programs with integrality constraints in the second stage we study continuity properties of the expected recourse as a function both of the first-stage policy and the integrating probability measure. Sufficient conditions for lower semicontinuity, continuity and Lipschitz continuity with respect to the first-stage policy are presented. Furthermore, joint continuity in the policy and the probability measure is established. This leads to conclusions on the stability of optimal values and optimal solutions to the two-stage stochastic program when subjecting the underlying probability measure to perturbations. (orig.)Available from TIB Hannover: RO 7722(429) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Computing gradients in parametrization-discretization schemes for constrained optimal control problems

General parametrization-discretization schemes for transforming constrained optimal control problems into finite-dimensional nonlinear programs are considered. Formulae for computing gradients of the objective and constraints are derived via adjoint systems and discussed for linear multistep and Runge-Kutta discretization schemes. These formulae require one integration of the state equation only. (orig.)SIGLEAvailable from TIB Hannover: RO 7722(508) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Prox-regularization approach for fully-parametrized convex semi-infinite programming problems Basic theory

For the class of fully-parametrized, ill-posed convex semi-infinite programming problems a solution scheme is developed which leads to numerically stable methods. This scheme consists in a coordinated application of adaptive discretization and prox-regularization procedures combined with a penalty method. On each iteration only an approximate minimum of a strongly convex differentiable function has to be calculated and this can be done by any fast-convergent algorithm. The use of the prox-regularization ensures convergence of the iterates to some solution of the original problem. Due to that regularization an efficient deleting rule is applicable, which excludes an essential part of the constraints in the discretized problems. (orig.)SIGLEAvailable from TIB Hannover: RO 7722(533) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Regularized penalty methods for optimal control of ill-posed elliptic systems

Application of prox-regularization to ill-posed stationary control problems is investigated. Stable variants of penalty methods with one-step and multi-step regularizations in the auxiliary problems are developed and their convergence is proved for distributed as well as boundary control problems with state constraints and Dirichlet or Neumann conditions. (orig.)SIGLEAvailable from TIB Hannover: RO 7722(522) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman