Gebze Technical University Mathematics Department Seminars

An Externally Controlled Problem for Heat Equation with Nonlocal Wentzell-Neumann Boundary Condition
Mansur I. Ismaliov
Gebze Teknik Üniversitesi, Turkey
Özet : We shall investigate the inverse source problem for the heat equation with the non-local Wentzell-Neumann boundary and the integral overdetermination conditions. Under some regularity, consistency and orthogonality conditions on the data, the existence, uniqueness and stability of the classical solution will be exhibited by using the generalized Fourier method. This study enables us to arrive at some conclusions on an externally controlled problem. The external energy is supplied to a target at a controlled level by the microwave generating equipment. The dielectric constant of the target material varies in space and time, this results spatially heterogeneous conversion of electromagnetic energy to heat which corresponds to the source term in form r(t)f(x,t). Here, r(t) is proportional to power of external energy source and f(x,t) is local conversion rate of microwave energy. It is necessary to notice that the spatial variation of absorbing material does not greatly affect the thermal diffusivity which is due to existence of another material at higher concentration. We additionally point out that the temperature is not so high, so that we may omit the temperature dependence of dielectric constant as in the case of thermal runaway studies. If u(x,t) denotes the concentration of absorbed energy, then its integral over all volume of material determines the time dependence absorbed energy. The inverse source problem for such a model gives an idea on how total energy content might be externally controlled when the boundary of the material is supported by the non-local Wentzell-Neumann boundary condition.
  Tarih : 07.04.2017
  Saat : 14:00
  Yer : Gebze Teknik Üniversitesi, Matematik Bölümü Seminer Odası
  Dil : English
  Ek Dosya : Özet