## Berichte der Arbeitsgruppe Technomathematik (AGTM Report)

### Filtern

#### Erscheinungsjahr

- 1992 (19) (entfernen)

#### Dokumenttyp

- Preprint (18)
- Wissenschaftlicher Artikel (1)

#### Volltext vorhanden

- ja (19) (entfernen)

#### Schlagworte

- 72
- A Mathematical Model for Diffusion and Exchange Phenomena in Ultra Napkins (1992)
- The performance of napkins is nowadays improved substantially by embedding granules of a superabsorbent into the cellulose matrix. In this paper a continuous model for the liquid transport in such an Ultra Napkin is proposed. Its mean feature is a nonlinear diffusion equation strongly coupled with an ODE describing a reversible absorbtion process. An efficient numerical method based on a symmetrical time splitting and a finite difference scheme of ADI-predictor-corrector type has been developed to solve these equations in a three dimensional setting. Numerical results are presented that can be used to optimize the granule distribution.

- 74
- On the Mróz Model (1992)
- We treat the mathematical properties of the one parameter version of the Mróz model for plastic flow. We present continuity results and an energy inequality for the hardening rule and discuss different versions of the flow rule regarding their relation to the second law of thermodynamics.

- 69
- Decoupling Normalizing Transformations and Local Stabilization of Nonlinear Systems (1992)
- A method of decoupling normalizing transformations has been developed. According to the method only the part of differential equations corresponding to the dynamic on a center manifold has to be modified by means of the normalizing transformations of a Poincare type. The existence of the normalizing transformation completely decoupling the stable dynamic from the center manifold dynamic has been proved. A numerical procedure for the calculation of asymptotic series for the decoupling normalizing transformation has been proposed. The developed method is especially important for the perturbation theory of center manifold and, in particular, for the local stabilization theory. In the paper some sufficient conditions for local stabilization have been given.

- 75
- Sensitivity of Luenberger Observers, e-Oberservability and Uncertainty Relations (1992)
- In this paper noises and disturbances are treated as distributions of some general class. The problem of sensitivity minimization is considered. A design procedure for the construction of Luenberger observers which estimate the state of a system with a given rate of accuracy has been proposed. The design procedure is applied to identify the first derivatives of an oscillating signal. The constraints on a noise and on a sampling which are necessary to estimate the derivatives to a given accuracy have been obtained.

- 84
- On a Transmission Boundary-Value Problem for the Time-Harmonic Maxwell Equations without Displacement Currents (1992)
- We consider a transmission boundary-value problem for the time-harmonic Maxwell equations neglecting displacement currents. The usual transmission conditions, which require the continuity of the tangential components of the electric and magnetic fields across boundaries are slightly modified. For this new problem we show that the uniqueness of the solution depends on the topological properties of the domains under consideration. Finally we obtain existence results by using a boundary integral equation approach.

- 86
- On the Equivalence of two Transmission Boundary-Value Problems for the Time-Harmonic Maxwell Equations without Displacement Currents (1992)
- We consider two transmission boundary-value problems for the time-harmonic Maxwell equations without displacement currents. For the first problem we use the continuity of the tangential parts of the electric and magnetic fields across material discontinuities as transmission conditions. In the second case the continuity of the tangential components of the electric field E is replaced by the continuity of the normal component of the magnetization B=müH. For this problem existence of solutions is already shown in [6]. If the domains under consideration are not simply connected the solution is not unique. In this paper, we improve the regularity results obtained in [6] and then prove existence and uniqueness theorems for the first problem by extracting its solution out of the set of all solutions of the second problem. Thus we establish a connection between the solutions corresponding to the different transmission boundary conditions.

- 68
- Stabilizability of Nonlinear Systems (1992)
- Elements of the differential topology are used to prove necessary conditions for stabilizability in large by a smooth feedback. Criteria for the smooth feedback stabilizing a smooth nonlinear system locally to have the smooth piecewise smooth extension, which stabilizes the system over a given compact set, have been obtained.

- 70
- A Random Discrete Velocity Model and Approximation of the Boltzmann Equation (1992)
- An approximation procedure for the Boltzmann equation based on random choices of collision pairs from a fixed velocity set and on discrete velocity models is designed. In a suitable limit, the procedure is shown to converge to the time-discretized and spatially homogeneous Boltzmann equation.

- 71
- The Broadwell Model in a Box: Strong L1-Convergence to Equilibrium (1992)
- The global solution of the one-dimensional Broadwell model in the interval [1,0], with reflecting boundary conditions at 0, is shown to converge strongly in L1[0,1] to the constant equilibrium solution.