Nonexistence for a boundary value problem arising in parabolic theory

The boundary value problemc _t=c _xx−c _yy+q(t,x)c with {fx349-1} was solved by Colton [1] forq analytic int. The solution may be used for mapping solutions of the heat equation into solutions ofu _t=u _xx+q(t,x)u. Solutions (of the boundary value problem) no longer exist ifq is not analytic int. Erica and Ludwig Jesselson Professor of Theoretical Mathematics, The Weizmann Institute of Science. This research was partially supported by the Minerva Foundation.