On prescribed change of profile for solutions of parabolicequations - Dokuchaev, Nikolai (IOP Publishing, 2011)
Parabolic equations with homogeneous Dirichlet conditions on the boundary are studied in a setting where the solutions are required to have a prescribed change of the profile in fixed time, instead of a Cauchy condition. It is shown that this problem is well-posed in L2-setting. Existence and regularity results are established, as well as an analog of the maximum principle.