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Carleman inequality and null controllability for parabolic equations. (English) Zbl 1316.93023
Article’s abstract (with reference expanded): “This paper is concerned with a detailed exposition on the Carleman inequality for a parabolic equation. Specifically, it represents only a part of the work of A. V. Fursikov and O. Yu Imanovilov [“Controllability of evolution equation”, Lecture Notes Series, Seoul. 34. Seoul: Seoul National Univ., (1996; Zbl 0862.49004)] for the particular model \(pt - \Delta p + f(p) = h\) of the heat equation. Moreover, we study the null controllability employing fixed-points for multi-valued mapping.”
93B05 Controllability
93C20 Control/observation systems governed by partial differential equations
35K20 Initial-boundary value problems for second-order parabolic equations
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics