On the backward heat problem: evaluation of the norm of ∂u∂t

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.

Bibliographic Details
Main Author: Yves Biollay
Format: Article
Language:English
Published: Hindawi Limited 1980-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171280000464

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