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

Yves Biollay

International Journal of Mathematics and Mathematical Sciences, 1980, vol. 3, 1-5

Abstract:

We show in this paper that ‖ Δ u ‖ = ‖ u t ‖ 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 ‖ u t ( x , T ) ‖ ≤ K .

Date: 1980
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:361874

DOI: 10.1155/S0161171280000464

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