International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 3, Pages 599-603
doi:10.1155/S0161171280000464
On the backward heat problem: evaluation of the norm of ∂u∂t
Department of Mathematics, Cornell University, Ithaca 14850, New York, USA
Received 19 July 1979
Copyright © 1980 Yves Biollay. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We show in this paper that ‖Δu‖=‖ut‖ is bounded ∀t≤T(0)<T if one imposes on u (solution of the backward heat equation) the condition ‖u(x,t)‖≤M. A Hölder type of inequality is also given if one supposes ‖ut(x,T)‖≤K.