On the backward heat problem: evaluation of the norm of
Yves Biollay · International Journal of Mathematics and Mathematical Sciences · 1980
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.