Email this article The Sobolev-type equations of the second order with the relatively dissipative operator pencils
- Authors: Zamyshlyaeva A.A1, Tsyplenkova O.N1
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Affiliations:
- South Ural State University (National Research University)
- Issue: Vol 16, No 2 (2012)
- Pages: 26-33
- Section: Articles
- URL: https://bakhtiniada.ru/1991-8615/article/view/20862
- ID: 20862
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Abstract
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.
About the authors
Alyona A Zamyshlyaeva
South Ural State University (National Research University)
Email: alzama@mail.ru
(к.ф.-м.н., доц.), докторант, каф. уравнений математической физики; Южно-Уральский государственный университет (национальный исследовательский университет); South Ural State University (National Research University)
Olga N Tsyplenkova
South Ural State University (National Research University)
Email: Tsyplenkova_Olga@mail.ru
аспирант, каф. уравнений математической физики; Южно-Уральский государственный университет (национальный исследовательский университет); South Ural State University (National Research University)
References
- Замышляева А. А. Фазовые пространства одного класса линейных уравнений соболевского типа второго порядка // Вычисл. технол., 2003. Т. 8, № 4. С. 45-54.
- Favini A., Yagi A. Degenerate differential equations is Banach spase / Pure and Applied Mathematics, Marcel Dekker. Vol. 215. New York, NY: Marcel Dekker, 1999. 312 pp.
- Showalter R. E. Monotone operators in Banach space and nonlinear partial differential equations / Mathematical Surveys and Monographs. Vol. 49. Providence, RI: American Mathematical Society, 1997. 278 pp.
- Sviridyuk G. A., Fedorov V. E. Linear Sobolev type equations and degenerate semigroups of operators / Inverse and Ill-Posed Problems Series. Vol. viii. Utrecht: VSP. 216 pp.
- Федоров В. Е. Сжимающие полугруппы уравнений соболевского типа и относительно диссипативные операторы // Мат. замет. ЯГУ, 2001. Т. 8, № 2. С. 75-83.
- Федоров В. Е. Обобщение теоремы Хилле-Иосиды на случай вырожденных полугрупп в локально выпуклых пространствах
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