Opuscula Math. 26, no. 1 (2006), 131-136
Opuscula Mathematica
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.
- 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
- Received: 2005-02-18.
