Boundary-value Problems with Non-local Initial Condition for Parabolic Equations with Parameter

In 2002, J.M. Rassias [14] imposed and investigated the bi-parabolic elliptic bi-hyperbolic mixed type partial differential equation of second order. In the present paper some boundary-value problems with non-local initial condition for model and degenerate parabolic equations with parameter were considered. Also uniqueness theorems are proved and non-trivial solutions of certain non-local problems for forward-backward parabolic equation with parameter are investigated at specific values of this parameter by employing the classical "a-b-c" method. Classical references in this field of mixed type partial differential equations are given by: J. M. Rassias [16] and M. M. Smirnov [25]. Other investigations are achieved by G.C. Wen et al. (in period 1990-2007).