By Karl Kunisch
Franz Kappel, 1940-2020. Photo courtesy of Bernd Thaller.
Franz Kappel, professor emeritus at the Institute of Mathematics and Scientific Computing at the University of Graz in Austria, passed away on April 3 during the early stages of the first local COVID-19 wave. He was a pioneer in the field of delay differential equations throughout the first part of his career, and made a substantial transition to research at the interface of mathematics and biomedical modelling in the second. He also mentored an impressive list of young researchers and engaged in university services in all possible ranks, having served as department head for 18 years, Dean for Science for six, and Vice-rector for Finance for four.
Franz was born in Graz, Styria, on Feb. 18, 1940. He earned his Ph.D. from the University of Graz in 1963 and his habilitation in 1970 from the Technical University of Graz, where he taught as an assistant professor until 1971. Franz then moved to Würzburg to work as a professor in the H.W. Knobloch’s group. Together, the two published the monograph Gewöhnliche Differentialgleichungen (Ordinary Differential Equations), which has remained a standard text for many generations of students.
I got to know Franz in an off-campus office at the University of Graz during the summer of 1975. He unpacked his books after returning from Würzburg, and I was looking for a Ph.D. advisor. I then had the tremendous fortune to be one of his pupils, as he led me with judicious care mathematically and thoughtfully guided me into scientific life on a personal level.
At the beginning of his academic career, Franz focused his attention on stability theory of dynamic systems in the spirit of Liapunov's direct method, as well as the Barbashin-Krasovskii-LaSalle invariance principle. He then moved on to the investigation of functional (delay-) differential equations, first systematically exploiting Laplace-transform techniques and establishing an elementary divisor theory before turning to approximation theory. Significant contributions include his seminal paper on spline approximation of delay differential equations with H.T. Banks (who also passed away recently and with whom Franz was good friends), his work on Riccati equations with D. Salomon, and his joint research on the abstract Trotter-Kato based schemes with K. Ito.
Throughout his career, Franz maintained a strong interest in mathematical modelling. He was the first professor to teach classes in our department that concentrated on bio applications. He also investigated population models—including features such as size or age structure—much earlier than most of the community. In the late 1990s, Franz distinctly moved towards cardiovascular modelling, including the respiratory system. His studies on modelling and subsequently controlling the dialysis process led to a fruitful collaboration with the Renal Research Institute in New York, which he frequently visited throughout his retirement. Franz enjoyed these visits since they provided an opportunity for him to push the limits of detailed modelling, as demanded by personalized medicine. They also gave him a reason to revisit the East Coast, which he had appreciated since his sabbatical at Brown University in 1977.
Franz provided significant services to the scientific community, as doing so came naturally. Many of his colleagues in control or semi-group theory likely remember the workshops organized in Retzhof, Vorau, and Mariatrost, which united leaders in their fields on a worldwide scale. Franz was also heavily involved with the ASEAN European Academic University Network; he advised Ph.D. students from Indonesia, Malaysia, and the Philippines, taught courses in these countries, and worked to bridge cultural gaps. During the course of these activities, as with many others, Franz had strong support from his wife Grit.
Franz Kappel was an inspiring person on diverse levels and is greatly missed by the Institute of Mathematics and Scientific Computing at the University of Graz, which he shaped for many years, and by his friends and colleagues worldwide.
Karl Kunisch is a professor in the Department of Mathematics at the University of Graz and scientific director at the Radon Institute of the Austrian Academy of Sciences in Linz.