Viktor Eckhaus

Viktor Eckhaus (born June 28, 1930 in Ivano-Frankivsk , † October 1, 2000 ) was a Dutch mathematician who dealt with differential equations. He was a professor at the University of Utrecht .

Life

Eckhaus came from a well-to-do family and grew up in Warsaw; his father ran a fur company. After the German occupation they had to hide as Jews in Poland. In 1947 the family came to Amsterdam via Austria. In 1948 he graduated from high school and studied aircraft technology at the Technical University of Delft . From 1953 to 1957 he worked in the National Aviation Laboratory in Amsterdam and from 1957 to 1960 he was at the Massachusetts Institute of Technology , where he received his doctorate in 1959 under Leon Trilling (Some problems of unsteady flow with discontinuities). In 1960 he became Maitre de Recherches at the Faculty of Mechanics at the Sorbonne . In 1964 he went to the University of Amsterdam and the Mathematical Center as a visiting professor and in 1965 he became a professor at the TU Delft. From 1972 until his retirement in 1994 he was a professor at the University of Utrecht .

He initially studied flows around airfoil profiles, which led him to investigate the stability of solutions of (weakly non-linear) systems of differential equations. Here the corner house instability criterion and the corner house instability are named after him, which appear as secondary instability, for example, in pattern-forming systems such as Rayleigh-Benard convection. Later he dealt with singular perturbation theory and most recently he dealt with soliton equations.

In 1983 he treated canards (translated as ducks , certain strongly singular oscillation relaxation phenomena) with standard methods of analysis, after this had previously been propagated by Marc Diener as an example of a problem that could only be treated with non-standard analysis.

In 1987 he became a member of the Royal Netherlands Academy of Sciences .

Fonts

• Studies in nonlinear stability theory, Springer Tracts in Natural Philosophy 6, 1965
• Matched asymptotic expansions and singular perturbations, North Holland 1973
• Asymptotic analysis of singular perturbations, North Holland 1979
• with Aart van Harten: The inverse scattering transformation and the theory of solitons. An introduction, North Holland 1981
• New approach to the asymptotic theory of nonlinear oscillations and wave propagation, J. Math. Anal. Appl., 49, 1975, 575-611
• Relaxation oscillations including a standard chase on french ducks, in: Asymptotic Analysis II, Lecture Notes in Mathematics, 985, Springer 1983
• The Ginzburg-Landau manifold is an attractor, J. Nonlinear Science, 3, 1993, 329-348
• with Eduard M. de Jager: Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type, Arch. Rat. Mech. Anal., 23, 1966, 26-86
• Witus en de jaren van angst: een reconstructie, editor Bas Lubberhuizen 1997 (autobiography)

literature

• Arjen Doelman, Hans Duistermaat, Johan Grasman, Aart van Harten In memoriam Wiktor Eckhaus , Nieuw Archief voor Wiskunde, March 2001, pdf