15. ÖMG-Kongress
Jahrestagung der Deutschen Mathematikervereinigung

16. bis 22. September 2001 in Wien

Sektion 7 - Funktionalanalysis, Harmonische Analysis
Dienstag, 18. September 2001, 16.30, Hörsaal 28

 

Semigroups in Colombeau generalized functions algebras

Danijela Rajter, University of Novi Sad (Koautoren: Stevan Pilipovic, Marko Nedeljkov)

 

Colombeau type semigroups determined by certain families of $C_0$-semigroups $(S_{\varepsilon})_{\varepsilon}$ with polynomial growth with respect to $\varepsilon$ are introduced and analysed. In the framework of generalized function algebras a general theory is applied to Cauchy problems $(\partial_{t}-\bigtriangleup) u +Vu = 0$, $u(0,x)=u_{0}(x)$, and $(\partial_{t}-\bigtriangleup) u +Vu +f(t,u) = 0$, $u(0,x)=u_{0}(x)$, where $V$ and $u_0$ are singular generalized functions and $f$ is at most of linear growth in $u$.

E-Mail:	danijela@mat1.uibk.ac.at
Homepage:	www.im.ns.ac.yu

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