The Solvability for a Class of Nonlinear Integrodifferential Equations of Parabolic Type (Journal of Partial Differential Equations, 1992)
In this paper we consider the well-posedness for a class of nonlinear integrodifferential equations of parabolic type. We use integral estimates to deduce an a priori estimate in the classical space C^{2+&#945,1+\frac{&#945}{2}}. The existence of the solution is established by means of the continuity method which is similar to a parabolic initial and boundary value problem. Moreover, the continuous dependence upon the data and the uniqueness of the solution are obtained. Finally, the results are generalized into a class of nonlinear integrodifferential systems.