Some analytical properties of dissolving operators related with the Cauchy problem for a class of nonautonomous partial differential equations. Part. 1

• Autorzy: Pytel-Kudela M. , Prykarpatsky A.K.
• Języki publikacji: EN

Abstrakty

EN

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 bilinear 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.

Słowa kluczowe

EN

dissolving operators; bilinear forms; Cauchy problem; semigroups; evolution equations

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2006
• Tom: Vol. 26, no. 1
• Strony: 131--136
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Pytel-Kudela M.

autor

Prykarpatsky A.K.

• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland,

Bibliografia

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• [3] Kato T., Perturbation theory for linear operators, Springer, 1966.
• [4] Chruściński D., Jamiołkowski A., Faza geometryczna: teoria i zastosowania, Toruń, 1996.
• [5] Bogoliubov N. N. (Jr.), Prykarpatsky A. K., Quantum method of generating Bogoljubov functionals in statistical physics: current Lie algebra, its representations and functional equations, Journal . Element. Particles and Atom Nucl. 17 (1986) (4), 789-827
• [6] Prykarpatsky A.K., Mykytiuk I.V.: Algebraic integrability of nonlinear dynamical systems on manifolds: classical and quantum aspects. Kluwer Academic Publishers, the Netherlands, 1998