Rudolf Gorenflo: a short outline of his
Born on 31 July 1930 in Friedrichstal near Karlsruhe,
1950 - 1956: student of Mathematics and Physics at Technical
University in Karlsruhe,
1956: diploma in mathematics,
1960: promotion to Dr. rer. nat. (doctor rerum naturalium),
1957 - 1961: scientific assistant at Technical University in Karlsruhe,
1961 - 1962: mathematician at Standard Electric Lorenz Company in Stuttgart,
1962 - 1970: research mathematician at Max-Planck Institute for Plasma
Physics in Garching near Munich,
1970: habilitation in mathematics at Technical University in Aachen,
1971 - 1973: professor at Technical University in Aachen,
1972: guest professor at University of Heidelberg,
since October 1973: full professor at Free University of Berlin,
1995: guest professor at University of Tokyo,
since October 1998: professor emeritus at Free University of Berlin.
Rudolf Gorenflo is member of several scientific associations.
Family status: married since August 1959, two sons, one daughter.
Fields of scientific work and interest
In my final student years (1950 - 1956) and in my time as as a scientific
assistant in Karlsruhe
(1957 - 1961) I was mainly interested in the theory of functions of one
complex variable, in particular in value distribution theory and growth
properties. This is documented in my diploma thesis Meromorphic periodic
functions of finite order and my doctoral thesis On the Wiman-Valiron
comparison method for power series and its application in the theory of
entire transcendental functions.
During my time in the department for informatics at Standard
Elektrik Lorenz in Stuttgart
(1961 - 1962) I was working in development of electronic calculating
machines. My main task was to devise simulation models for distant booking
systems. This required investigation and use of pseudo- random numbers, Monte Carlo methods and theory of queues, and so I had
opportunity to acquire some expertise in these matters.
For my work as a research mathematican in the Theory Department of the Max
Planck Institute for Plasma-Physics in Garching near Munich
(1962 - 1970) my knowledge of complex analysis (from my time in Karlsruhe) and of electronic computing machines (from my
time in Stuttgart)
were extremely useful. My principal activities were distributed on three
(1) application of complex analysis to plane problems of
magneto-hydro-statics and stationary magneto-hydro-dynamics,
(2) application of Monte Carlo methods for simulation of particle flights in
a rarefied gas,
(3) numerical analysis, in particular theory and application of difference
schemes to ordinary and partial differential equations (e.g. for large scale
computation of magnetic fields), furthermore numerical methods for evaluation
of spectroscopic measurements (in the rotationally symmetric case via Abel
As leader of a group of mathematicians and computer programmers I was
responsible for consulting and asssisting physicists and engineers in the
mathematical and numerical treatment of their problems.
During my time in Aachen (1970 - 1973) and
(since) 1973 for several years I divided my research interests between (a)
integral equations (mainly of Abel type) and the neighboring subject of
inverse and ill-posed problems and (b) difference schemes for parabolic
In (a) this led to my book with Sergio Vessella on Abel Integral Equations:
Theory and Applications, Lecture Notes in Mathematics 1461,
Later, as can be seen from my list of publications, this work was (in
collaboration with co-authors) extended to inverse problems in heat
conduction, asymptotic properties of singular values, nonlinear inverse
problems, problems of recovery of a function from knowledge of its moments.
In (b), a field which I had begun already in the Max Planck Institute, I
carried out my particular intention to develop and investigate difference
scheme that imitate essential properties of the diffusion processes that were
modelled, namely properties of conservation of mass or energy, preservation
of non-negativity, damping properties. In this way, the obtained difference
schemes allow a double interpretation, namely (i) as that of a process of
discrete redistribution of an extensive quantity on the grid-points, (ii) as
that of a random walk discrete in space and time, of a particle wandering
according to a diffusion process described by the parabolic equation at hand.
The connection between these two interpretations lies in the fact that
probability itself can be viewed as an extensive quantity.
In 1992 (stimulated by a research visit to Prof. R. Rutman at University
of Massachusetts in Dartmouth) I began working on ordinary fractional
differential equations and related special functions, and later
(beginning in 1995) I intensified this work in collaboration with Prof. F.
Mainardi and other investigators. Soon these interests were extended to cover
partial fractional equations (fractional in time or in space or in both time
and space), equations suitable for modelling non-classical diffusion
processes. In this collaboration various types of random walk models were
devised and analyzed. For me personally, this activity is a fascinating
generalization of my earlier investigations, see (b) above, of difference
schemes conserving mass or non-negativity (or energy) in classical diffusion
processes. Present interests are also in applications of such processes.
As it can be seen from my list of publications
I have been especially active in international cooperations, having in particular
co-authors from People’s Republic of China, Israel,
Italy, Japan, former Soviet Union,
United States, Vietnam
as long term visitors.
Under my principal guidance the folllowing candidates have been promoted
to Dr. rer. nat.:ì
Matthias Blumenfeld (1983) with his thesis Eigenlösungen von gemischten
Interface-Problemen auf Gebieten mit Ecken: ihre Regularität und
Approximation mittels finiter Elemente.
Dinh Nho Hào aus Hanoi,
(1991) with his thesis Inverse heat conduction problems.
Christine Kutsche (1994) with her thesis Produktquadraturverfahren
für nichtglatte Lösungen Abelscher Integralgleichungen,
Evelyn Buckwar (1996) with her thesis Iterative
approximation of the positive solutions of a class of nonlinear Volterra-type
Gabriela Witte (1997) with her thesis Die analytische und
nmerische Behandlung einer Klasse von Volterraschen Integralgleichungen in
Talaat El Danab (1998) aus Shibin El-Koom, Ägypten,
with his thesis Efficient and accurate numerical methods for Burgers’ equation
and related partial differential equations,
Alain Roger Nkamnang (1999) aus Yaoundé, Kamerun, with his
thesis Diskretisierung von mehrgliedrigen Aelschen Integralgleichungen und
gewöhnlichen Differentialgleichungen gebrochener Ordnung.