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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

international journal of mathematics and mathematical sciences

On the backward heat problem: evaluation of the norm of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$\frac{{\partial u}} {{\partial t}}$" id="E1"><mml:mrow><mml:mfrac><mml:mrow><mml:mo>∂</mml:mo><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mo>∂</mml:mo><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:math>

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