Petak, 07. april 2006. u 14h, sala 2 MI SANU BG:

Lubin G. Vulkov, Rousse University, Bulgaria
DISCRETE MAXIMUM PRINCIPLE (MP) AND SOME ITS APPLICATIONS TO PROBLEMS WITH INTERFACES AND BLOW-UP

Abstract: Maximum and comparison principles are fundamental properties of PDEs of second order. There are different formulations of these properties. They hold for variety of linear and nonlinear problems. Thinking about numerical solution of PDEs satisfying the maximum or comparison principle, there arises a natural question, whether these principles are satisfied also on a discrete level. Of course, they are not satisfied in general. It depends on the used method. In the present lecture we discuss two applications of the discrete MP. The first one concerns the construction of finite difference schemes for heat-diffusion equations with singular own sources that satisfy the discrete MP. Convergence proof is provided and numerical experiments are discussed. The second one concerns elliptic equations with nonlinear boundary conditions of parabolic type. Continuous and semidiscrete blow-up solutions of these problems are analyzed on the base of maximum and comparison principles.

Petak, 14. april 2006. u 14h, sala 2 MI SANU:

akademik Vojislav Maric, T. Kusano
O JEDNOJ KLASI FUNKCIONALNIH DIFERENCIJALNIH JEDNA?INA SA SPORO PROMENLJIVIM RE^ĘENJIMA

Sadr^Ţaj: Daju se potrebni i dovoljni uslovi da bi jedna klasa takvih jedna?ina imala sporo promenljiva re^Úenja u smislu Karamate.

Petak, 21. april 2006. u 14h, sala 2 MI SANU:

NERADNI DAN

Petak, 28. april 2006. u 14h, sala 718, MF BGD:

Luigi Rodino, University of Torino, Italy
GELFAND-SHILOV FUNCTION SPACES AND APPLICATIONS

Abstract: We present new applications of Gelfand-Shilov classes. In particular, we observe that partial differential equations in Quantum Mechanics, of Schroedinger type, admit solutions in these classes. Moreover, solitary solutions (travelling waves) of relevant nonlinear partial differential equations of the Mathematical Physics belong to Gelfand-Shilov spaces. Other applications concern Time-Frequency analysis and localization operators.