### SOBOLEV TYPE EQUATION IN (n,p)-SECTORIAL CASE

#### 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.

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