Seminars

Logarithmic norms and Quadratic forms with applications to Calculus of Variations

Időpont:
2019. 02. 21. 10:15
Hely:
H306
Gustaf Söderlind

The logarithmic norm was introduced in 1958 for matrices, and for the purpose of estimating growth rates in initial value problems. Since then, the concept has been extended to nonlinear maps, differential operators and function spaces. There are applications in operator equations in general, including evolution equations as well as boundary value problems. The logarithmic norm is the extremal value of a quadratic form.

In this talk we outline how logarithmic norms of differential operators can be computed, and how they are related to variational calculus and ellipticity. Thus, while one typically seeks the minimizing function in a variational problem, the logarithmic norm is the corresponding extremal value of the functional associated with a particular symmetrized differential operator. There are also connections to eigenvalue problems for selfadjoint and non-selfadjoint operators. This will also be illustrated with an application to classical singular problems, such as the Bessel equation, as well as to the biharmonic operator.

A vákuum Einstein-egyenlet megoldhatósága nem kompakt 4-sokaságokon

Időpont:
2019. 02. 19. 10:30
Hely:
H306
Etesi Gábor

On some qualitative properties of parabolic problems

Időpont:
2019. 02. 14. 10:15
Hely:
H306
Horváth Róbert

In this talk we investigate some special qualitative properties of parabolic problems. At the beginning of the talk we review the remarkable qualitative properties of these problems. Then we will turn to two special properties: the first property says that the number of the so-called LL-level points, or specially the number of the zeros, of the solutions must be non-increasing in time. The second property requires a similar property for the number of the local maximizers and minimizers. We show that linear equations and some special nonlinear equations fulfill the above properties in the continuous case. We use the maximum-minimum principles in the proof. Then we generate the numerical solution with the implicit Euler finite difference method and show that the obtained numerical solution satisfies the discrete versions of the above properties without any requirements on the mesh parameters. We show also some numerical test results.

Horváth Róbert előadása a Farkas Miklós Szemináriumon

Időpont:
2019. 02. 14. 10:15
Hely:
BME H. épület 306-os terem
Horváth Róbert- BME

The use of copulas to model non-Gaussian distributed multivariate data

Időpont:
2019. 01. 16. 14:15
Hely:
BME H. épület 306-os terem
Krzysztof Domino Institute of Theoretical and Applied Informatics, PAS, Gliwice

Jacobi triple product via the exclusion process

Időpont:
2019. 01. 10. 16:15
Hely:
H306