Equadiff 82: Proceedings of the international conference held in Würzburg, FRG, August 23–28, 1982

688 Pages·1983·12.19 MB·English

by  Wolfgang Alt, Micah Dembo (auth.), H. W. Knobloch, Klaus Schmitt (eds.)

Lecture Notes ni
Mathematics
Edited yb .A Dotd and .B Eckmann
7101
Equadiff 82
Proceedings of the international conference
held ni FRG, W(Jrzburg, August 23-28, 1982
Edited yb H.W. Knobloch and .K Schmitt
II
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Berlin Heidelberg New York oykoT 1983
Editors
H.W. Knobloch
Mathematisches Institut, Universit~it WQrzburg
Am Hubland, 8700 W~irzburg, Federal Republic of Germany
Klaus Schmitt
Department of Mathematics, The University of Utah
Salt Lake City, Utah 84112, USA
AMS Subject Classifications (1980): Main: 34 A-K
Related: 35B, 70A-L, ?6A-R, 92A10, 92A1 5
ISBN 3-540-12686-4 Springer-Verlag Berlin Heidelberg New York Tokyo
ISBN 0-387-12686-4 Springer-Verlag New York Heidelberg Berlin Tokyo
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Preface
The international conference EQUADIFF 82 was held at the Univer-
sity of WHrzburg during the week August 23 to August 28, 1982. It was
the fourth in a sequence of international conferences, with focus on
the subject of differential equations, which were started in 1970 in
Marseille by the late Professor Vogel and then continued in Brussels
in 1973 and Florence in 1978.
The program of the conference was prepared by the Scientific
committee consisting of R.Conti, W.N.Everitt, J.K.Hale, W.J~ger,
J.Kurzweil, J.Mawhin, J.Moser, M.Roseau, K.Schmitt and T.Yoshizawa.
All other organizational responsibilities were shared by P.Hagedorn,
H.W.Knobloch, H.Kielh~fer, R.Reissig and W.Werner. The official spon-
sors of the conference were:
Deutsche Forschungsgemeinschaft
and
Bayerisches Staatsministerium
fHr Unterricht und Kultus.
In keeping with the tradition set by the earlier conferences the
scientific committee decided to emphasize the following subjects as
conference topics:
Ordinary differential equations, Functional differential equations,
Stochastic differential equations, Partial differential equations of
evolution type and Difference equations.
Since interest among nonexperts in a highly specialized conference
such as EQUADIFF 82 a( name which in German is anything but self-
explanatory) could not a priori be assumed, the organizers gratefully
acknowledge that all institutions and persons contacted for assistance
were most willing to cooperate. Not only was support received from the
official sponsors but also from the administration of the University
of W~rzburg, whose president, Professor Theodor Berchem, and vice-
president, Professor Martin Lindauer, showed great interest in the
conference. The organizers are particularly indebted to them.
The addition of the number 82 to the title of the conference is a devia-
tion from earlier custom. This was done to indicate that the conference
was part of the official program set up to celebrate the founding of
the University of W~rzburg in the year 1582. This linkage with the
fourth centenary celebration of the host institution added a special
VI
accent to the conference, particularly to the social program. For this
reason a few remarks about the history of the University of WHrzburg
and about science and mathematics there seem to be in order in these
proceedings.
The University of W~rzburg was founded as a typical "confessional"
university during the course of the great religious conflicts of the
sixteenth century. That it did not disappear again - as did many other
universities - at the end of the middle ages is mainly due to the
common sense and realistic assessment of the value of higher education
which the founder of the university and some of his successors had. In
the opening decree the rSle of the university was viewed in a remark-
ably modern way: Above all it should provide the opportunity to acquire
knowledge without the necessity to move to distant places or of paying
high costs.
Medicine was the first discipline which benefited from the ideas of
the founder and first rector of the university. Later - during the age
of Enlightenment - his successor freed the faculty of Philosophy from
the influence of the Jesuit order. This was the first step in develo-
ping a modern faculty of liberal arts and science in WOrzburg. The most
outstanding and best-known of the many scientific achievements attri-
buted to its members perhaps is the discovery of x-rays by W.C.R~ntgen
in 1895.
During the 18th and 19th century mathematics, astronomy and theo-
retical physics were represented by the same chair in WHrzburg as was
the case in many smaller European universities. As a result mathema-
tical activities were naturally somewhat limited until the middle of
the nineteenth century. The rise of modern physics and chemistry then
gave new impetus also to mathematics. A second chair was created and
given to F.Prym, a student of B.Riemann. His successful efforts to
spread and interpret the ideas of his great teacher have influenced
the development of modern mathematical thinking in Germany.
The historical alliance between mathematics, astronomy and mecha-
nics during the early history of European science has contributed much
to our present knowledge about structures and methods in the theory of
differential equations. These roots are still visible in the theory of
dynamical systems, a mathematical discipline which encompasses the
various topics covered by EQUADIFF 82. The present day notion of a
dynamical system is in a very general sense a model of some real system
fX
Dafermos, C.M. Lefschetz Center for Dyn. Systems,
Brown University, Box F,
Providence, R.I. o2912, ASU
de Pascale, .E Dipartimento di Matematica, Universita
della Calabria, 1-87o36 Arcavacata di edneR
Italy
Dijksma, A. Mathematisch Instituut, Rijksuniversiteit
Groningen, Postbus 8oo, oo79-LN VA Groningen
Netherlands
Djaja, .C Zahumska 42, YU-11o5o Beograd, Yugoslavia
Doden, KI. Mathematisches Seminar, Christian-
Albrecht-Universit~t Kiel,
Olshausenstra~e 4o-6o, Haus S 12a,
D-23oo Kiel 1, Germany
Dominguez, .B Facultad ed Matematicas, Universidad ed
Sevilla, c/Tarifia s/n, Sevilla, Spain
Eberhard, .W Universit~t Duisburg, Mergelskull 52
D-415o Krefeld, Germany
Edelson, oA Dept. of Mathematics, Univers. of Cali-
fornia, Davis, Cal. 95616, ASU
Engler, .H Inst. f. Angew. Mathem., Universit~t
Heidelberg, mI Neuenheimer Feld 392
D-69oo Heidelberg, Germany
Erbe, L. Dept. of Mathem., Univers. of Alberta,
Edmonton, Alberta G6T 2GI, Canada
Farkas, .M Dept. of Mathem., Budapest Univers.
of Technology, H-1521 Budapest, Hungary
Farwig, .R Inst. fur Angew. Mathem., Universit~t
Wegelerstr. 6, D-53oo Bonn I, Germany
Feny~, I. Dept. of Mathem., Technical University
Stoczek u. 2, H-1111 Budapest, Hungary
Fiedler, B. Sonderforschungsbereich 123, Universit~t
mI Neuenheimer Feld 293, D-69oo HeideIbe~
Germany
Flockerzi, .D Mathem.lnstitut der Universit~t WUrzburg
mA Hubland, D-87oo WUrzburg, Germany
Freedman, H.I. Dept. of Mathem., University of Alberta
Edmonton, Alberta G6T 2G1, Canada
Freiling, .G BF Ii- Mathematik, Universit~t-Gesamt-
hochschule, Lotharstra~e 65,
D-41oo Duisburg I, Germany
Fryszkowsik, A. Institute of Mathematics, Technical Univ.
PI. J. Robotniczej i, PI-oo-661 Warszawa
Poland
which may be distinguished from its environment and which evolves in
time according to some inherent dynamics. The rSle of dynamical systems
is hence very similar to the one played by ordinary differential equa-
tions in classical mechanics. If one wishes to describe it in simple
terms, one is tempted to use almost the same phrases which once were
used to describe the merits of university education: By studying the
structure of dynamical systems one can gain insight into the real world
which otherwise could be obtained only at high cost and at "distant
times", that is, through expensive and time consuming experiments.
Progress in computer science gives more and more credence to this
statement, since it opens new possibilities of exploiting highly com-
plex theoretical results for practical purposes. For this reason the
tradition of previous EQUADIFF conferences was carried further and also
numerical methods and applications in engineering, physics and biology
were represented by special sections in the program.
The conference, which was attended by over 200 scientists from
27 different countries, demonstrated clearly the ever increasing inter-
national cooperation in the area of dynamical systems. Cooperation bet-
ween various institutions was also necessary in order to establish the
framework for the scientific program. We here record with gratitude
the assistance which we received from the following institutions:
Mathematisches Institut der Universit~t W~rzburg,
Sonderforschungsbereich "Stochastische Mathematische
Modelle", Heidelberg,
Sonderforschungsbereich "Approximation und Mathematische
Optimierung", Bonn,
Department of Mathematics, University of Utah.
The first three institutions shared the organizational aspects of the
conference and the last took on the preparation of these proceedings.
Special thanks are also due to the secretaries
Mrs. Ingrid B6hm and Mrs. Isolde Brugger, WHrzburg and
Mrs. Jackie S.Hadley, Salt Lake City
for their invaluable contributions.
WHrzburg and Salt Lake City, March 1983
The Editors.
A_ddress list of participants
Allegretto, .W Dept. of Mathematics, University of
Alberta, Edmonton,Alberta G6T 2G1,Canada
Alt, .W Sonderforschungsbereich 123, Universit~t
mI Neuenheimer Feld 293, D-69oo Heidelberg
Germany
Ambrosetti, A. International School for Advanced
Studies (S.I.S.S.A.) Strada Costiera,11
1-34014 Trieste, Italy
Appel, J. Istituto Matematico "Ulisse Dini",
Universita di Fireoze, Viale Morgagni,
1-50134 Firenze, Italy
Arino, .O
Dept. ed Math~matiques, Universit~ ed
Pau, Avenue ed L. Sallenave, 64ooo Pau,
France
Arndt, .H Institut fur Angewandte Mathematik,
Universit~t, Wegelerstr.6, D-5300 Bonn
Germany
Arnold, L. Fachbereich Mathematik, Universit~t
Postfach, D-2800 Bremen 33, Germany
Aronsson, .G Dept. of Mathematics, University of Lulea
S-95187 Lulea, Sweden
Aulbach, B. Mathematisches Institut, Universit~t
mA Hubland, D-87oo WUrzburg, Germany
Balser, .W Abt. Mathematik V, Universit~t mlU )HNM(
D-7900 Ulm, Germany
Barbanti, L. MAT-IME-USP, Cidade Universitaria,
Cx. Postal 2o.57o, o55o8 oaS Paulo (SP)
Brazil
Bardi, .M Istituto di Analisi e Meccanica, Univ.
di Padova, Via Belzoni 7, 1-351oo avodaP
Italy
Bellen, A. Istituto di Matematica, Universita di
Trieste, 1-341oo Trieste, Italy
Besjes, J.G. Dept. of Mathematics, Technological
University Delft, Julianalaan 231
NL-2728 LB Delft, Netherlands
Beyn, W.-J. Fakult~t fur Mathematik,Universit~t
Jacob-Burckhardt-Str.17, o577-D Konstanz,
Germany
Binding, P.A. Dept. of Mathem., University of Calgary
Calgary, Alberta N2T 1N4, Canada
IIIV
Bobrowski, .D Mathematical Institute, Politechnika
Poznanska, .wS Rocha 6-A-7,
PI-61-142- Poznan, Poland
Boudourides, .M Dept. of Mathematics,Democritus Univer-
sity of Thrace, Xanthi, Greece
Braaksma, B.L.J. Mathematisch Instituut, Rijksuniversiteit
Groningen, Postbus 8oo, NL-97oo VA Gronin-
gen, Netherlands
Braess, .D Mathem.lnstitut, Ruhr-Universit~t,
Universit~tsstr. 15o, D-463o Bochum 1,
Germany
Brunovsky, .P Institute of Applied Mathematics,
Comenius University, Mlynska dolina
842 51 Bratislava, Czechoslovakia
van der Burgh, A.H.P. Dept. of Mathematics, Technological
University Delft, Julianalaan 231
NL-2628 LB Delft, Netherlands
Canada, V. Dept. de Ecuaciones Funcionales Facul-
tad de Ciencias, Granada, Spain
Capozzi, A. Istituto di Matematica Applicata
Universita degli Studi di Bari, Via
eR David, 2oo/A, I-7o125 Bari, Italy
Caristi, .G Istituto di Matematica, Universita di
Trieste, Piazzale Europa 1, 1-341oo Trieste
Italy
ed Castro, .A Facultad ed Matematicas, Universidad de
Sevilla, Sevilla-12, Spain
Cerami, .G Istituto di Matematica, Universita di
Palermo, Via Archirafi 34,
I-9o123 Palermo, Italy
Cesari, L. Dept. of Mathematics, University of
Michigan, nnA Arbor, Mich. 481o4, ASU
Conley, .hC Dept. of Mathematics, University of
Wisconsin, naV Vleck Hall, o84 Lincoln
Drive, Madison, Wisc. 537o6, ASU
Conti, .R Istituto Matematico "Ulisse Dini"
University degli studi, Viale Morgagni
67/A, I-5o134 Firenz, Italy
Couot, J. REU Math., Universite Paul Sabatier
811 Route de Narbonne, F-31o77 Toulouse
Cedex, France
Cree, G.C. Dept. of Mathematics, ehT University
of Alberta, Edmonton, Alberta G6T 1G2
Canada
Crespin, .D Dept. of Matematicas, P.O.Box 615,
Caracas IoI-A, Venezuela
Furumochi, T. Dept. of Mathem., lwate University,
Ueda 3-18-33, Morioka City o2o, Japan
Gambaudo, J.M. Mathem. Dept., I.M.S.P., Universite de
Nice, Parc Valrose, F-o6o34 Nice, France
Georgiou, .D Dept. of Mathem., Democritus University
of Thrace, Xanthi, Greece
van Gils, St. Stichting Mathematisch Centrum,
Kruislaan 413, NI-lo98 JS Amsterdam,
Netherlands
Graef, J.R. Dept. of Mathem., Mississippi State
University, P.O. Drawer AM
Mississippi State, SM 39762, ASU
Grasman, J. Dept. of Applied Mathematics,
Mathematical Centre, Jruislaan 413,
NI-Io98 JS Amsterdam, Netherlands
Gripenberg, .G Institute of Mathematics, Helsinki
University of Technology,
SF-o215o Espoo 15, Finland
Gro#mann, .U Max-Planck-lnstitut fur Systemphysiologie
Rheinlanddamm 2ol, D-46oo Dortmund I,
Germany
Gumowski, I. UER-Math.,Universite Paul Sabatier,
118, Route de Narbonne, F-31o62 Toulouse
France
Habets, .P Universite Catholique ed Louvain
2, Chemin ud Cyclotron, B-1348 Louvain-
la-Neuve, Beglium
Haddock, J.R. Dept. of Mathem. Sciences, Memphis
State University, Memphis, nT 38152,USA
Hagedorn, P. Institut fur Mechanik, Technische Hoch-
schule, Hochschulstra~e 1, D-61oo Darm-
stadt, Germany
Hainzl, J. Gesamthochschule/Universit~t Kassel
Kaulenbergstr. 8, D-35oo Kassel,Germany
Halbach, .U Zoologisches Institut der Universit~t
Siesmayerstra~e 7o, D-6ooo Frankfurt/M.
Germany
na der Heiden, .U Universit~t WN 2, D-28oo Bremen 33,
Germany
Heil, E. BF Mathem., Techn.Hochschule,
SchloBgartenstr.7, D-61oo Darmstadt,
Germany
XI
Herold, .H BF Mathematik, Universit~t, Lahnberge
D-355o Marburg, Germany
Hino, Y. Bept. of Mathematics, Chiba University,
1, Yayoicho, Chiba 26o, Japan
Hoppensteadt, F.C. Dept. of Mathematics, The University of
Utah, Salt Lake City, Utah 84112, ASU
Hornung, ,U BF 15, Mathematik, Universit~t, Einstein-
straBe 62, D-44oo MUnster, Germany
Howes, F.A. Dept. of Mathem., Univers. of California
Davis, AC 95616, ASU
Hueber, .H Fakult~t fur Mathematik, Universit~t
Bielefeld, Postfach 864o, D-48oo Biele-
feld, 1, Germany
lannacci. .R Dipartimento di Matematica, Universita
della Calabria, 1-87o36 Arcavacata di
Rende, Italy
Invernizzi, .S Istituto di Matematica, Universita di
Trieste, 1-341oo Trieste, Italy
Ize, A.F. Instituto de Ciencias Matematicas,
ed oaS Carlos, Caixa Postal 668,
1356o oaS Carlos (Sao Paulo),Brazil
Ize, J. IIMAS, U.N.A.M, Apartado Postal 2o-726
olooo Mexico o2 D.F., Mexico
J~ger, .W Sonderforschungsbereich 123, Universit-
t~t, mI Neuenheimer Feld 293,
D-69oo Heidelberg, Germany
Jeggle, .H Fachbereich 3/Mathematik/MA6-3,
Technische Universit~t, Strafe des
17. Juni 135, D-looo Berlin 12, Germany
Joseph, D.D. Dept. of Aerospace Engineering and
Mechanics, Iio Union Street S.E.
Minneapolis, Minnesota 55455, ASU
Kaminogo, T. Mathematical Institute, Tohoku Univers,
Sendai 98o, Japan
Kappel, F. Institut fur Mathematik, Karl-Franzens-
Universit~t, Elisabethstra~e 11,
A-8olo Graz, Austria
Karim, R.I.IoA. Mathematics Dept., King Saud University
P,O. soB 2455, Riyad, Saudi Arabia
Kato, J. Mathem. Institute, Tohoku University
Sendai 98o, Japan
Kawohl , B. Inst. fur Angew. Mathem., Universit~t
Martenstr. 3, D-852o Erlangen, Germany
Keller, B. Koenig & Bauer, Friedrich-Koenig-Str.4
D-87oo WUrzburg, Germany