Аннотации:
The linear model of plane-parallel thermal convection in a viscoelastic incompressible
Kelvin Voigt material amounts to a hybrid of the Oskolkov equations and the heat equations in the Oberbeck Boussinesq approximation on a two-dimensional region with B enard's conditions. We study the solvability of this model with the so-called multipoint initial- nal conditions. We use these conditions to reconstruct the parameters of the processes in question from the results of multiple observations at various points and times. This enables
us, for instance, to predict emergency situations, including the violation of continuity of
thermal convection processes as a result of breaching technology, and so forth.
For thermal convection models, the solvability of Cauchy problems and initial- nal
value problems has been studied previously. In addition, the stability of solutions to the
Cauchy problem has been discussed. We study a multipoint initial- nal value problem for
this model for the rst time. In addition, in this article we prove a generalized decomposition
theorem in the case of a relatively sectorial operator. The main result is a theorem on the unique solvability of the multipoint initial- nal value problem for the linear model of planeparallel
thermal convection in a viscoelastic incompressible uid.
Описание:
S.A. Zagrebina, South Ural State University, Chelyabinsk, Russian Federation,
zagrebina_sophiya@mail.ru. Софья Александровна Загребина, кафедра "Дифференциальные и стохастические уравнения", Южно-Уральский государственный университет (г. Челябинск, Российская Федерация), zagrebina_sophiya@mail.ru