Approximate controllability of the burgers equation with impulses and delay
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.
Publication Source (Journal or Book title)
Far East Journal of Mathematical Sciences
Leiva, H., & Sundar, P. (2017). Approximate controllability of the burgers equation with impulses and delay. Far East Journal of Mathematical Sciences, 102 (10), 2291-2306. https://doi.org/10.17654/MS102102291