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Stability of partial functional integro-differential equations. (English) Zbl 1178.35368

Summary: Using 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.

MSC:

35R09 Integro-partial differential equations
35B35 Stability in context of PDEs
93C20 Control/observation systems governed by partial differential equations
45K05 Integro-partial differential equations
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