About the existence and uniqueness of strong solution of the antiperiodic problem for the heat equation with deviating argument

Abstract

In this paper we have proved the strong solvability of a mixed problem for the heat equation with deviating argument and with the antiperiodic homogeneous boundary conditions u_t(x, T-t)+u_xx(x, t)=f(x, t), u^|_t=0=0, u^|_x=0+u^|_x=l=u_x^|_x=0+u_x^|_x=l=0, in the space L₂(Ω).