Abstract
In this paper, we consider an impulsive homogeneous parabolictype partial integro-differential equation with degenerate kerneland involution. With respect to spatial variable \(x\) is usedDirichlet boundary value conditions and spectral problem isstudied. The Fourier method of separation of variables is applied.The countable system of nonlinear functional equations is obtainedwith respect to the Fourier coefficients of unknown function.Theorem on a unique solvability of countable system of functionalequations is proved. The method of successive approximations isused in combination with the method of contraction mapping. Theunique solution of the impulsive mixed problem is obtained in theform of Fourier series. Absolutely and uniformly convergence ofFourier series is proved.
