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, no. 2 (2012), pp. 26-33

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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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     title = {The {Sobolev-type} equations of the second order with the relatively dissipative operator pencils},
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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, no. 2 (2012), pp. 26-33. http://geodesic.mathdoc.fr/item/VSGTU_2012_2_a2/