Solvability of an Initial–Boundary Value Problem for a Parabolic Equation with a Time-Nonlocal Term in Hölder spaces

Abstract

We consider an initial–boundary value problem for a semilinear parabolic differential equation with a time-nonlocal term. This term contains the integral of the solution over the entire time interval on which the problem is considered. The solvability of the problem in Hölder classes is proved. The uniqueness of the solution is established under a constraint on the length of the time interval over which the solution is integrated in the nonlocal term.