Geodesic
The Sobolev-type equations of the second order with the relatively dissipative operator pencils
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 127 (2012) no. 2, pp. 26-33 Cet article a éte moissonné depuis la source Math-Net.Ru

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Of concern is the Cauchy problem for the Sobolev-type equation of the second order. We introduce the definition of relatively dissipative operator pencils, generalize the notion of dissipativity and relative dissipativity of operators. The connection with the theory of accretive operators is established. According to the Keldysh ideology, the original problem is reduced to the Cauchy problem for the Sobolev-type equation of the first order and the results for the investigated problem are obtained.
Mots-clés : Sobolev-type equation
Keywords: relative dissipativity of the operator pencil, accretive operators, phase space. 
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A. A. Zamyshlyaeva; O. Tsyplenkova. The Sobolev-type equations of the second order with the relatively dissipative operator pencils. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 127 (2012) no. 2, pp. 26-33. http://geodesic.mathdoc.fr/item/VSGTU_2012_127_2_a2/

[1] Zamyshlyaeva A. A., “Phase spaces of some class of linear second-order Sobolev-type equations”, Vychisl. Tekhnol., 8:4 (2003), 45–54 | Zbl

[2] Favini A., Yagi A., Degenerate differential equations is Banach spase, Pure and Applied Mathematics, Marcel Dekker, 215, Marcel Dekker, New York, NY, 1999, 312 pp. | MR | Zbl

[3] Showalter R. E., Monotone operators in Banach space and nonlinear partial differential equations, Mathematical Surveys and Monographs, 49, American Mathematical Society, Providence, RI, 1997, 278 pp. | MR | Zbl

[4] Sviridyuk G. A., Fedorov V. E., Linear Sobolev type equations and degenerate semigroups of operators, Inverse and Ill-Posed Problems Series, viii, VSP, Utrecht, 216 pp. | MR | Zbl

[5] Fedorov V. E., “Contracting semigroups of Sobolev-type equations and relatively dissipative operators”, Mat. Zamet. YaGU, 8:2 (2001), 75–83 | Zbl

[6] Fedorov V. E., “A generalization of the Hille-Yosida Theorem to the case of degenerate semigroups in locally convex spaces”, Siberian Math. J., 46:2 (2005), 333–350 | DOI | MR | Zbl