Parabolic equations with the second-order Cauchy conditions on the boundary - Dokuchaev, Nikolai (IOP Publishing, 2007)
The paper studies some ill-posed boundary value problems on semi-plane for parabolic equations with the homogenous Cauchy condition at initial time and with the second-order Cauchy condition on the boundary of the semi-plane. A class of inputs that allows some regularity is suggested and described explicitly in the frequency domain. This class is everywhere dense in the space of square integrable functions.