In this paper an ill-posed problem for the heat equation is investigated. Solutions u to the equation u_t— u_xx= 0, which are approximately known on the positive half-axis t = 0 and on some vertical lines x = x,,…,x = x„, are considered and stability estimates of these solutions are presented. We assume an a priori bound, governing the heat flow across the boundary x = 0.
A NOTE ON AN ILL-POSED PROBLEM FOR THE HEAT EQUATION / G. TALENTI; S. VESSELLA. - In: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS. - ISSN 0263-6115. - STAMPA. - 32:(1982), pp. 358-368. [10.1017/S1446788700024915]
A NOTE ON AN ILL-POSED PROBLEM FOR THE HEAT EQUATION
TALENTI, GIORGIO;VESSELLA, SERGIO
1982
Abstract
In this paper an ill-posed problem for the heat equation is investigated. Solutions u to the equation u_t— u_xx= 0, which are approximately known on the positive half-axis t = 0 and on some vertical lines x = x,,…,x = x„, are considered and stability estimates of these solutions are presented. We assume an a priori bound, governing the heat flow across the boundary x = 0.
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