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Approximate controllability of the burgers equation with impulses and delay

Abstract:

In this paper, we prove the interior approximate controllability of the following Burgers equation under the influence of impulses and delay: (Formula Presented) where (Formula Presented), ω is an open nonempty subset of (0, 1), 1ω denotes the characteristic function of the set ω and the distributed control u belongs to L2 ([0, τ]; L2[0, 1]). We prove the following statement: If the functions f, Jk are smooth enough, then the system is approximately controllable on [0, τ], for all τ > 0. In this case, the delay helps us to prove the approximate controllability by pulling back the control solution to a fixed curve in a short time interval.