- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 15:07:12
7
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=ZAA&vol=9&iss=3&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)
9
1990
3
A Stabilization Method for the Tricomi Problem
N.A.
Lar'kin
Institute for Theoretical and Applied Mechanics, NOVOSIBIRSK, RUSSIAN FEDERATION
M.
Schneider
Karlsruher Institut für Technologie (KIT), KARLSRUHE, GERMANY
We prove the existence of a generalized solution of the Tricomi problem for the equation $L_0[u] = T[u] + \lambda l (u) := yu_{zz} + u_{yy} + \lambda 1 (u) = f$, where $l = \alpha^1 \partial /\partial x + \alpha^2 \partial / \partial y$ is a special differential operator and $\lambda ≥ 0$ is a constant. Then we show the solvability of an initial boundary value problem for the evolution equation $L[u] = T[u] + \partial (u)/ \partialt = F$ by an aproximation method. It is shown that the generalized solution of the evolution problem converges to the generalized solution of the Tricomi problem $T[u] = f$ as $t \to \infty$. The rate of convergence is estimated.
General
193
202
10.4171/ZAA/394
http://www.ems-ph.org/doi/10.4171/ZAA/394
Perturbation of Temperature Fields by a Small Inclusion
Dietrich
Göhde
, LEIPZIG, GERMANY
In a domain which contains a small subdomain $\Omega_{\epsilon}$ a boundary value problem of second order with transition conditions on the boundary of $\Omega_{\epsilon}$ is posed. For its solution an asymptotic expansion is constructed with respect to the diameter of $\Omega_{\epsilon}$ tending to zero.
General
203
212
10.4171/ZAA/395
http://www.ems-ph.org/doi/10.4171/ZAA/395
Approximation durch Lösungen elliptischer Randwertprobleme auf nichtglatten Gebietsrändern
Uwe
Hamann
Universität Rostock, ROSTOCK, GERMANY
Let $\Omega \subset \mathbb R^n$ be a bounded, smootI domain and $\Gamma$ the (not necessary smooth) boundary of an open set $\Omega_i \subset \subset \Omega$. it is investigated, under which conditions given tuples of continuous functions (Whitney-Taylorfields) on $\Gamma$ can be uniformly approximated by solutions of elliptic boundary value problems with respect to $\Omega$.
General
213
220
10.4171/ZAA/396
http://www.ems-ph.org/doi/10.4171/ZAA/396
Factoring Compact Operators and Approximable Operators
Ioan Mircea
Popovici
High School Mircea cel Batrin, CONSTANTZA, ROMANIA
Dan Tudor
Vuza
Romanian Academy, BUCHAREST, ROMANIA
Our paper is concerned with two topics. The first one is represented by aversion of Figiel’s and Johnson’s theorem on the factorization of compact operators adapted to the framework of ordered Banach spaces. Namely, we prove that every compact operator from a Banach space to an ordered Banach space with closed generating cone (respectively, a Banaöh lattice) factors, with compact factors, through a reflexive lattice-ordered Banach space with closed generating cone, the second factor being positive (respectively, a reflexive lattice-ordered Banach space with continuous modulus, the second factcr being a Riesz homomorphism). The second topic is provided by a discussion of the factorization of approximable operators between :Banach lattices. We prove that every such operator $U$ factors through a reflexive Banach lattice with an unconditional basis, the factors being compact and one of them being positive. We also give a necessary and sufficient condition on $U$ under which both factors in the mentioned factorization can be taken to be differences of positive compact operators.
General
221
233
10.4171/ZAA/397
http://www.ems-ph.org/doi/10.4171/ZAA/397
Investigation of extremals in a generalized isoperimetric problem by means of higher-order conditions
N.P.
Osmolovskii
, MOSCOW, RUSSIAN FEDERATION
The problem of a material point going round maximum area on a plane in a fixed period of time, with its velocity vector varying in a compact set $U$, is considered. Under some assumptions on $U$ and with the help of higher-order conditions it is proved that multiply-traversing extremals do not even give a so-called 0-weak maximum (which would at the same time be a weak maximum in the case of continuous velocity). For simply traversing extremals providing an absolute maximum; a non-trivial result on the kind of the maximum is obtained. Furthermore, finite-dimensional and infinite-dimensional quadratic forms connected with the pointed-out generalizationof the isoperimetric problem are studied; their non-negativeness on the corresponding subspaces and some other properties are established.
General
235
272
10.4171/ZAA/398
http://www.ems-ph.org/doi/10.4171/ZAA/398
Die Struktur der Extremallösungen von linearen Differentialgleichungen $n$-ter Ordnung
Vratislav
Pudei
, PARDUBICE, CZECH REPUBLIC
The structure of extremal solutions of linear ordinary differential equations of order $n$ on an interval $[t_0, \eta (t_0)]$ is shown, where $\eta (t_0)$ is the first conjugate point of $t_0$. It is also shown by it, how this structure depends on the number of linearly independent extremal solution.
General
273
275
10.4171/ZAA/399
http://www.ems-ph.org/doi/10.4171/ZAA/399
Monotonicity Properties of Oscillatory Solutions of Second Order Differential Equations
Erich
Müller-Pfeiffer
Pädagogische Hochschule, ERFURT, GERMANY
It is proved in what way monotonicity properties of the coefficients of ordinary second order differential equations are transmitted to oscillatory solutions $u$ of such equations. For instance, there are statements on the distances of the zeros of $u$, $u’$, and $u$ and $u’$ mutually.
General
277
288
10.4171/ZAA/400
http://www.ems-ph.org/doi/10.4171/ZAA/400