Viktor K. Andreev, Ilona A. Reznikova, “The estimates of solutions of adjoint heat problem in spherical area”, J. Sib. Fed. Univ. Math. Phys., 2012, Volume 5, Issue 4,Pages <nobr>485

The estimates of solutions of adjoint heat problem in spherical area

Viktor K. Andreev^a, Ilona A. Reznikova^b

^a Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk, Russia
^b Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia

Abstract: Spherically symmetric adjoint initial-boundary value problem of heat propagation in closed bounded spherical regions has been researched. A priori estimates of temperature have been obtained subject to internal heat sources. Friedrichs inequality has been generalized for such areas.

Keywords: initial-boundary value problem, a priori estimates, Green function, interface.

UDC: 512.54

Received: 05.04.2012
Received in revised form: 05.05.2012
Accepted: 10.06.2012