On the backward heat problem: evaluation of the norm of ∂u∂t - Yves Biollay (International Journal of Mathematics and Mathematical Sciences)
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.