Boundary and initial boundary-value problems for separable backward–forward parabolic problems

A backward–forward parabolic equation is considered in a strip which is infinite in the timelike direction, with boundary conditions on the sides of the strip. The unique bounded solution of the problem is given explicitly by separation of variables. In addition, a similar problem in a semi-infinite strip is treated, with initial data at the end of the strip. It is shown that the solution can be represented arbitrarily closely in the maximum norm by a sum of functions obtain by separation of variables.