Journal of Siberian Federal University. Mathematics & Physics / On an Ill-Posed Problem for the Heat Equation

Full text (.pdf)
Issue
Journal of Siberian Federal University. Mathematics & Physics. 2012 5 (3)
Authors
Puzyrev, Roman E.; Shlapunov, Alexander A.
Contact information
Puzyrev, Roman E. : Institute of Mathematics, Siberian Federal University , Svobodny, 79, Krasnoyarsk, 660041, Russia , e-mail: ; Shlapunov, Alexander A. : Institute of Mathematics, Siberian Federal University , Svobodny, 79, Krasnoyarsk, 660041, Russia , e-mail:
Keywords
boundary value problems for heat equation; ill-posed problems; integral representation's method
Abstract

A boundary value problem for the heat equation is studied. It consists of recovering a function, satisfying the heat equation in a cylindrical domain, via its values ant the values of its normal derivative on a given part of the lateral surface of the cylinder. We prove that the problem is ill-posed in the natural spaces of smooth functions and in the corresponding Holder spaces; besides, additional initial data do not turn the problem to a well-posed one. Using Integral Representation's Method we obtain Uniqueness Theorem and solvability conditions for the problem.

Pages
337-348
Paper at repository of SibFU
https://elib.sfu-kras.ru/handle/2311/2924