Opuscula Math. 26, no. 1 (2006), 131-136
Some analytical properties of dissolving operators related with the Cauchy problem for a class of nonautonomous partial differential equations. Part 1
Marzena Pytel-Kudela
Anatoliy K. Prykarpatsky
Abstract.
The analytical properties of dissolving operators related with the Cauchy problem for a class of nonautonomous partial differential equations in Hilbert spaces are studied using theory of bi-linear forms in respectively rigged Hilbert spaces triples. Theorems specifying the existence of a dissolving operator for a class of adiabatically perturbed nonautonomous partial differential equations are stated. Some applications of the results obtained are discussed.
Keywords:
dissolving operators, bilinear forms, Cauchy problem, semigroups, evolution equations.
Mathematics Subject Classification:
34B15, 35B12, 46T15.
About the authors ▼
Marzena Pytel-Kudela
AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland
Anatoliy K. Prykarpatsky
AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland
About the article ▼
Received: 2005-02-18.
Cite this article as ▼
Marzena Pytel-Kudela, Anatoliy K. Prykarpatsky, Some analytical properties of dissolving operators related with the Cauchy problem for a class of nonautonomous partial differential equations. Part 1, Opuscula Math. 26, no. 1 (2006), 131-136,
http://dx.doi.org/10.7494/OpMath.2006.26.1.131.
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