Outline
DOI: 10.7494/opmath.2006.26.1.131 ISSN: 1232-9274
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. PrykarpatskyThe 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.
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