Abstract:
We consider a mathematical model of thermoelastic plate vibrations under certain assumptions. The model is based on the nonclassical high-order equation of the mathematical physics. In addition, this equation is unsolvable with respect to the time derivative of higher order. In appropriately chosen functional spaces, the considered mathematical model can be reduced to an abstract Sobolev type equation of the third order with relatively (n,p)-sectorial operator on the right-hand side. As is known, an equation of Sobolev type is not solvable for arbitrary initial values. Therefore, we construct a set of admissible initial values. The main research approach is the method to construct resolving groups.
Keywords:
Sobolev type equation, relatively spectral-bounded operator, bundle of operators, mathematical model of thermoelastic plate vibrations.
\Bibitem{BycKot17}
\by E.~V.~Bychkov, K.~Yu.~Kotlovanov
\paper Sobolev type equation in $(n, p)$-sectorial case
\jour J. Comp. Eng. Math.
\yr 2017
\vol 4
\issue 2
\pages 66--72
\mathnet{http://mi.mathnet.ru/jcem92}
\crossref{https://doi.org/10.14529/jcem170207}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3670942}
\elib{https://elibrary.ru/item.asp?id=29454747}
Linking options:
https://www.mathnet.ru/eng/jcem92
https://www.mathnet.ru/eng/jcem/v4/i2/p66
This publication is cited in the following 1 articles:
Anar T. Assanova, “Solvability to an initial-periodic problem for delay partial differential equations of Sobolev type”, Quaestiones Mathematicae, 46:9 (2023), 1751
Citation in format AMSBIB
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