Parabolic equations with the second order Cauchy conditions on the boundary
arXiv:0708.1978 · doi:10.1088/1751-8113/40/41/010
Abstract
The paper studies some ill-posed boundary value problems on semi-plane for parabolic equations with homogenuous 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 frequency domain. This class is everywhere dense in the space of square integrable functions.
arXiv comment7 pages