An inverse coefficient problem for quasilinear pseudo-parabolic heat conduction of polymeric materials


Bağlan İ. , Canel T.

International Conference on Mathematics and Mathematics Education, Konya, Türkiye, 11 - 13 Temmuz 2019, cilt.1, no.1, ss.208-209

  • Cilt numarası: 1
  • Basıldığı Şehir: Konya
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.208-209

Özet

The inverse problem of determining unknown coefficient in a quasi-linear

parabolic equation has generated an increasing amount of interest from engineers

and scientist. The problem of recovering unknown source function in the

mathematical model of a physical phenomena is frequently encountered. These

problems were studied by many scientists with different boundary conditions (Cannon

1988, Pourgholia 2010, Ford 1973, Li 2015). The problem proposed in this study can

be used in many application such as investigation of heat distribution on laser

material interaction. In this article, we worked with periodic boundary conditions

unlike others. Moreover, from a technical point of view, these boundary conditions

are more difficult. This condition was studied by (Baglan 2010,Baglan 2014,Halilov

2009) with different direct problems. Also, in this article, we worked with pseudoparabolic

inverse problem.

Consider the problem of finding a pair of functions (a,u) satisfying the following

quasilinear pseudo-parabolic problem:

In this research, we examine an inverse problem of a quasilinear pseudoparabolic

equation with periodic boundary condition.We consider the initial-boundary