On problems for singular parabolic systems without initial conditions
- 33 Downloads
We consider a boundary-value problem without initial conditions for B -parabolic systems that contain even-order derivatives with respect to the space variable. For the problem under study, we obtain an integral representation of its solution via the Green function. In this representation, we take into account the restrictions by time imposed on the boundary functions and the inhomogeneity of the system. We also obtain a representation of the solution of a model boundary-value problem with the help of Poisson kernels and establish conditions for the existence of this solution.
KeywordsHeat Conduction Equation Parabolic System Poisson Kernel Liouville Theorem Bessel Operator
Unable to display preview. Download preview PDF.
- 2.M. I. Konarovska, “Liouville theorems for singular parabolic systems,” Scientific Bulletin of Chernivtsi University: Series Mathematics [in Ukrainian], Issue 485 (2009), pp. 28–34.Google Scholar
- 4.M. I. Matiichuk, Parabolic Singular Boundary-Value Problems [in Ukrainian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv (1999).Google Scholar
- 8.S. D. Eidel’man, Parabolic Systems [in Russian], Nauka, Moscow (1964).Google Scholar
- 9.M. Bokalo, “Dynamical problems without initial conditions for elliptic-parabolic equations in spatial unbounded domains,” Electron. J. Different. Equat., No. 178, 1–24 (2010).Google Scholar