Global theorem of existence and uniqueness of the first boundary value problem for nonlinear integrodifferential equations of parabolic type

Global theorem of existence and uniqueness of solution of the first boundary value problem for nonlinear integrodifferential equation of parabolic type is proved. If the right-hand side of the equation is integrally bounded, then we have estimate of the norm of the difference of two solutions, which implies continuous dependence of solution on the initial function and uniqueness of solution of the first boundary value problem. The problem under consideration generalizes the real model for measuring the level of incompressible fluid in the fuel tanks missiles. Therefore, such problem have a current application.