Stability of partial functional integro-differential equations

Using the Fourier method of separation of variables and a procedure proposed in this paper, namely, reducing integrodifferential equations to systems of ordinary differential equations, the exponential stability of partial functional integro-differential equations is studied. Various tests for the exponential stability are proposed. In contrast to many other known methods our approach does not assume the smallness of integral terms. This allows us to use the method for stabilization of processes described by unstable differential equations by adding controls in the form of integral terms. Finally, using our approach, a phase transition model is analyzed.