Opuscula Mathematica

Opuscula Math.
 26
, no. 1
 (), 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



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.
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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ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
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