ON A CLASS OF NONLINEAR PARABOLIC EQUATIONS WITH NONLINEAR TRACE TYPE FUNCTIONALS

In this paper we consider a class of non-classical parabolic equations in which some nonlinear trace type functionals are involved. The motivation for our investigation arises from the determination of some unknown nonlinear functions in parabolic equations. We employ the Schauder fixed point theorem to prove the existence of solutions. We also study the regularity property of solutions. Moreover, the continuous dependence upon the known data as well as uniqueness of the solution is established.