Stability of Partial Functional Integro-Differential Equations

Authors:
R. P. Agarwal;A. Domoshnitsky;Ya. Goltser
Affiliations:
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, USA 32901;Department of Mathematics and Computer Sciences, The College of Judea and Samaria, Ariel, Israel 44837;Department of Mathematics and Computer Sciences, The College of Judea and Samaria, Ariel, Israel 44837
Venue:
Journal of Dynamical and Control Systems
Year:
2006

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Abstract

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.