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Approximate controllability of a parabolic equation with memory. (English) Zbl 1238.93018

Summary: We study the approximate controllability of a parabolic equation with memory \(y_t + y_{xx} + \int^t_0 y(x,s)ds = 0\) by boundary control. The proof relies on the explicit solution of the corresponding homogeneous initial boundary value problem and a duality method.

MSC:

93B05 Controllability
93C20 Control/observation systems governed by partial differential equations
35R09 Integro-partial differential equations
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