- Diese Veranstaltung hat bereits stattgefunden.
November-Sitzung der Klasse Naturwissenschaften
14. November 2013 - 10:00 - 12:00
Die Klasse Naturwissenschaften lädt zur planmäßig am 14. November 2013 stattfindenden November-Sitzung ein, auf der der folgende Vortrag gehalten und zur Diskussion gestellt wird:
Peter Holota (MLS):
Boundary Problems of Mathematical Physics in Earth’s Gravity Field Studies
BVV-Saal, 10:00 bis 12:00 Uhr
Dr. Holota is geodesist and mathematician. Since 2013 he is a member of the Leibniz Society. In 1969 he graduated in geodesy (geodetic astronomy) at the Czech Technical University, Prague. In 1976 he graduated in mathematics at the Charles University, Prague and here he got his RNDr. (Rerum naturalium doctoris) degree in 1982. His DrSc. (Doctor scientiarum) degree he received at the Czechoslovak Academy of Sciences in 1987. In 1970 he started his career at the Research Institute of Geodesy, Topography and Cartography. The area of his research is theoretical and physical geodesy and mathematical methods for studies of the Earth’s gravitational field. He is the secretary of the Czech National Committee of Geodesy and Geophysics and is also engaged in university teaching. In 1987-1999 he was elected the secretary and then the president of the IAG (International Association of Geodesy) section on General theory and methodology. In 1995-1999 he was a member of the IAG Executive Committee and in 1999-2003 the president of the IAG special commission on Mathematical and physical foundations of geodesy. Within the IAG he organized several scientific symposia and a number of scientific sessions. Since 2008 under the umbrella of the EGU (European Geosciences Union) he annually convenes sessions on Recent developments in geodetic theory. In 1989-2005 he was subsequently a member of the Editorial Boards of Manuscripta geodaetica, Bulletin Géodésique and Journal of Geodesy published by the IAG. In addition he is an Associate Editor in Studia Geophysica et Geodaetica, Bolletino di Geofisica Teorica ed Applicata and zfv – Zeitschrift für Geodäsie, Geoinformation und Landmanagement. In 1985-1986 he was awarded the Alexander von Humboldt research fellowship at the Department of Geodetic Science, University of Stuttgart. In 2003 he was an external examiner at the University of Calgary. In 1991 he was awarded the honorary title ‘a Fellow of the IAG’. He is also a member of EGU and AGU (American Geophysical Union). His biography is included in several Czech and international ‘Who’s Who’ publications.
Studies on Earth’s gravity field enable to learn more about our planer. The motivation considered here comes primarily from geodetic applications. We particularly focus on the related mathematics and mathematical tools that form the basis for this research. Historical milestones and famous figures of science in this field are briefly recalled equally as the notion of potential and its first definition. The theory of boundary value problems for elliptic partial differential equations of second order, in particular for Laplace’s and Poisson’s equation, offer a natural basis for gravity field studies, especially in case they rest on terrestrial measurements. Various kinds of free, fixed and mixed boundary value problems are considered. Concerning the linear problems, the classical as well as the weak solution concept is applied. Free boundary value problems are non-linear and are discussed separately. The complex structure of the Earth’s surface makes the solution of the boundary problems rather demanding. Some techniques, that may solve these difficulties, are shown. Also an attempt is made to construct the respective Green’s functions, reproducing kernels and entries in Galerkin’s matrix for the solution domain given by the exterior of an oblate ellipsoid of revolution. The integral kernels are expressed by series of ellipsoidal harmonics and their summation is discussed. Possibilities of using the concept of boundary-value problems for studies that rest on terrestrial gravity measurements in combination with satellite data on gravitational field are considered too. An optimization approach is applied together with the methods above, as the problems to be solved are overdetermined by nature. Finally some questions and stimuli are discussed that are related to physical and mathematical models of the problems mentioned in this contribution.