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Obstruction and some approximate controllability results for the Burgers equation and related problems. (English) Zbl 0853.93014
Casas, Eduardo (ed.), Control of partial differential equations and applications. Proceedings of the IFIP TC7/WG-7.2 international conference, Laredo, Spain, 1994. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 174, 63-76 (1996).
The paper studies the approximate controllability for the Burgers equation. Due to the presence of a superlinear term, an obstruction phenomenon arises which implies a lack of approximate controllability in spaces of type \(L^p\) or \(C\). However, the author is able to prove several controllability results under suitable constraints on the desired state. Finally, a necessary condition for the approximate controllability of the Navier-Stokes system on a rectangle is given.
For the entire collection see [Zbl 0834.00041].
Reviewer: O.Cârjá (Iaşi)

93B05 Controllability
93C20 Control/observation systems governed by partial differential equations