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.

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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

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