- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 06:24:58
5
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=ZAA&vol=1&iss=5&update_since=2024-03-29
Zeitschrift für Analysis und ihre Anwendungen
Z. Anal. Anwend.
ZAA
0232-2064
1661-4534
Partial differential equations
Ordinary differential equations
Integral equations
Numerical analysis
10.4171/ZAA
http://www.ems-ph.org/doi/10.4171/ZAA
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2006)
1
1982
5
Die Methode der Grenzschichtverbesserung für eine Masse entarteter gewöhnlicher Differentialgleichungen
Sybille
Meyer
Technische Universität Chemnitz, CHEMNITZ, GERMANY
In this paper we generalize Visik’s and Ljusternik’s method for a symptotic solution of boundary value problems with a small parameter in the highest derivatives of the differential equation for a class of boundary value problems for non-self-adjoint ordinary differential equations of the order $2m$, in which the coefficients have a zero of integer order in a boundary point. A part of the arising boundary layer equations having singularities. In Chapter 3 of this paper we calculate the index of the differential operators of this boundary layer equations in a certain pair of spaces of the positive half-axis. In Chapter 4 we construct the first term of an asymptotic solition for small parameter values.
General
1
15
10.4171/ZAA/32
http://www.ems-ph.org/doi/10.4171/ZAA/32
Gleichmässige asymptotische Darstellungen für Parameterintegrale mit zwei reellen Parametern
Hans-Joachim
Schell
Technische Universität Chemnitz, CHEMNITZ, GERMANY
Several asymptotic approximations, valid uniformly on certain $\alpha$-intervals, are obtained for a class of integrals depending on two real parameters s and $\alpha$, where $s$ tends to $s_0$. Two cases are considered: a) the integrand has a simple maximum interior to the interval of integration, b) the interval of integration contains no stationary point. In both cases the results still hold true if the stationary point coalesces with the lower limit of integration.
General
17
27
10.4171/ZAA/33
http://www.ems-ph.org/doi/10.4171/ZAA/33
The Galerkin method for parabolic equations with operators of local type (in Russian)
Peeter
Oja
Tartu University, TARTU, ESTONIA
The existence and the uniqueness of solution are investigated for the Cauchy problem $u’(t) + A(t) u(t) + (Mu) (t) = f(t), u(0) = u_0$, with a family of linear operators $A(t)$ and a local typo operator $M$. In the applications $M$ represents, in particular, the retardation of the argument or an integral operator. It is shown that this Cauchy problem produces an isomorphism between some natural spaces of given data and solutions. The convergence of the Galerkin method takes place in strong norms containing derivatives by$ $t. The rate of convergence is characterized by two-sided estimates. The influence of perturbations, arising in the course of calculating the coefficients of the approximate problem as scalar products, on the approximate solutions is given also by two-sided estimates in the same norms in which the convergence is proved.
General
29
51
10.4171/ZAA/34
http://www.ems-ph.org/doi/10.4171/ZAA/34
Nonlinear noncoercive equations and applications
Pavel
Drábek
University of West Bohemia, PLZEN, CZECH REPUBLIC
This paper deals with the periodic solvability of the nonlinear beam equation $$\beta u_t + u_{tt} + u_{xxxx} - \lambda u + \varphi (u) = f,$$ which depends on non-linear $\varphi : \mathbb R \to \mathbb R$. This paper continues the subject of the paper by S. Fucik [6]. We present some new methods and results which are not included in [6].
General
53
65
10.4171/ZAA/35
http://www.ems-ph.org/doi/10.4171/ZAA/35
Über ein Bimetallproblem in der Ebene
Lothar
Jentsch
Technische Universität Chemnitz-Zwickau, CHEMNITZ, GERMANY
Existence and uniqueness theorems for boundary-contact-problems of plane elastostatics and thermoelastostatics are given in a proper class of regularity, when the thermoelastic constants are piecewise constant and discontinuous along a straight line. The problem is reduced with the aid of the contact-tensor of elastostatics for two composite half-planes to a system of integral equations with fixed singularities. From the theory of Duduchava it follows, that the integral operator is Noetherian in the space $L_2(S)$ ($S$ boundary of the disc) with index zero.
General
67
92
10.4171/ZAA/36
http://www.ems-ph.org/doi/10.4171/ZAA/36