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.