## Search

Now showing items 11-20 of 53

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Preprint
Convergence analysis of time-discretization schemes for rate-independent systems

(2017-12-21)

It is well known that rate-independent systems involving nonconvex energy
functionals in general do not allow for time-continuous solutions even if the
given data are smooth. In the last years, several solution concepts were
proposed that include discontinuities in the notion of solution, among them
the class of global energetic solutions and the class of BV-solutions.
In general, these solution concepts are not equivalent and numerical schemes
are needed that reliably approximate that type of solutions ...

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Preprint
Balanced Viscosity solutions to a rate-independent system for damage

(2017-05-02)

This article is the third one in a series of papers by the authors on
vanishing-viscosity solutions to rate-independent damage systems. While in the
first two papers [KRZ13, KRZ15] the assumptions on the spatial domain $\Omega$
were kept as general as possible (i.e. nonsmooth domain with mixed boundary conditions), we
assume here that $\partial\Omega$ is smooth and that the type of boundary
conditions does not change. This smoother setting allows us to derive enhanced regularity spatial properties both for ...

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Preprint
A free boundary approach to the Rosensweig instability of ferrofluids

(2017-04-18)

We establish the existence of saddle points for a free boundary problem describing the two-dimensional free surface of a ferrofluid which undergoes normal field instability (also known as Rosensweig instability). The starting point consists in the ferro-hydrostatic equations for the magnetic potentials in the ferrofluid and air, and the function describing their interface. The former constitute the strong form for the Euler-Lagrange equations of a convex-concave functional. We extend this functional in order to ...

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Preprint
On the existence of symmetric minimizers

(2018-01-23)

In this note we revisit a less known symmetrization method for functions with respect to a topological group, which we call G-averaging. We note that, although quite non-technical in nature, this method yields G-invariant minimizers of functionals satisfying some relaxed convexity properties. We give an abstract theorem and show how it can be applied to the p-Laplace and polyharmonic Poisson problem in order to construct symmetric solutions. We also pose some open problems and explore further possibilities where the ...

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Preprint
Mathematical problem solving, modelling, applications, and links to other subjects

(1989)

The paper will consist of three parts. In part I we shall present some background
considerations which are necessary as a basis for what follows. We
shall try to clarify some basic concepts and notions, and we shall collect
the most important arguments (and related goals) in favour of problem solving,
modelling and applications to other subjects in mathematics instruction.
In the main part II we shall review the present state, recent trends, and
prospective lines of development, both in empirical or theoretical ...

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Preprint
On the equivariant Tamagawa number conjecture for abelian extensions of a quadratic imaginary field

(Universität Kassel, FB 17, Mathematik/Informatik, 2005)

Let k be a quadratic imaginary field, p a prime which splits in k/Q and does not divide the class number hk of k. Let L denote a finite abelian extention of k and let K be a subextention of L/k. In this article we prove the p-part of the Equivariant Tamagawa Number Conjecture for the pair (h0(Spec(L)),Z[Gal(L/K)]).

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Preprint
A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it

(2005)

In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.

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Preprint
Modellierung und numerische Simulation der Thermoregulation von Früh- und Neugeborenen

(Universität Kassel, FB 17, Mathematik/Informatik, 2005)

Bei frühgeborenen Säuglingen spielt die Thermoregulation zur Aufrechterhaltung einer überlebenswichtigen Körpertemperatur durch Wärmeproduktion, -abgabe bzw. -aufnahme eine entscheidende Rolle. Der Einsatz moderner Inkubatoren soll die körpereigenen Thermoregulatoren unterstützen, und es ist im Hinblick auf verschiedene medizinische Fragestellungen wünschenswert, diesen Prozess modellieren zu können. Wir stellen ein einfaches Modell auf der Basis von partiellen Differentialgleichungen vor und beschreiben detailliert ...

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Preprint
Asymptotics of number fields and the Cohen-Lenstra heuristics

(Universität Kassel, FB 17, Mathematik/Informatik, 2005)

We study the asymptotics conjecture of Malle for dihedral groups Dl of order 2l, where l is an odd prime. We prove the expected lower bound for those groups. For the upper bounds we show that there is a connection to class groups of quadratic number fields. The asymptotic behavior of those class groups is predicted by the Cohen-Lenstra heuristics. Under the assumption of this heuristic we are able to prove the expected upper bounds.

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Preprint
Error estimates for approximate approximations on compact intervals

(2005)

The aim of this paper is the investigation of the error which results from the
method of approximate approximations applied to functions defined on compact in-
tervals, only. This method, which is based on an approximate partition of unity, was introduced by V. Mazya in 1991 and has mainly been used for functions defied on the whole space up to now. For the treatment of differential equations and boundary integral equations, however, an efficient approximation procedure on compact intervals is needed.
In the ...