An Initial Boundary Value Problem for Parabolic Differential-Operator Equations

AbstractIn this paper we give, for the first time, an abstract interpretation of such initial boundary value problems for parabolic equations that a part of boundary value conditions contains also a differentiation on the time t. Initial boundary value problems for parabolic equations are reduced to the Cauchy problem for a system of parabolic differential-equations [see below problems (1)–(3)]. A solution of this system is not a vector-function but one function. At the same time, the system is not overdetermined