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Abstract
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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

Yves Biollay

Department of Mathematics, Cornell University, Ithaca 14850, New York, USA

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.