Exact controllability for semilinear parabolic equations with Neumann boundary conditions

This paper studies the problem of exact boundary controllability of second-order semilinear parabolic equations when the control is under Neumann's boundary conditions. For a nonlinear term with a sublinear growth we prove the global null-controllability and for the superlinear growth case we prove the local exact controllability of the equations.

[1]  G. Lebeau,et al.  Contróle Exact De Léquation De La Chaleur , 1995 .

[2]  J. Lions,et al.  Contrôlabilité exacte des systèmes distribués , 1986 .

[3]  D. I. Piotkovskii.  COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY: On the growth of graded algebras with a small number of defining relations , 1993 .

[4]  Thomas I. Seidman,et al.  Two results on exact boundary control of parabolic equations , 1984 .

[5]  D. Russell.  Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Questions , 1978 .

[6]  W. Littman,et al.  Null boundary controllability for semilinear heat equations , 1995 .

[7]  J. Aubin,et al.  Applied Nonlinear Analysis , 1984 .

[8]  Oleg Yu. Imanuvilov,et al.  On Controllability of Certain Systems Simulating a Fluid Flow , 1995 .

[9]  Andrei V. Fursikov,et al.  Local exact controllability of the Navier-Stokes equations , 1996 .

[10]  H. O. Fattorini,et al.  Boundary Control of Temperature Distributions in a Parallelepipedon , 1975 .

[11]  V. Tikhomirov,et al.  Optimal Control , 1987 .

[12]  O. Ladyženskaja.  Linear and Quasilinear Equations of Parabolic Type , 1968 .

[13]  A. Fursikov,et al.  Exact boundary zero controllability of three-dimensional Navier-Stokes equations , 1995 .

[14]  J. Lions.  Exact controllability, stabilization and perturbations for distributed systems , 1988 .

[15]  Irena Lasiecka,et al.  Exact controllability of semilinear abstract systems with application to waves and plates boundary control problems , 1989 .

[16]  Jean-Pierre Puel,et al.  Approximate controllability of the semilinear heat equation , 1995, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[17]  O. Oleinik,et al.  GENERALIZED ANALYTICITY AND SOME RELATED PROPERTIES OF SOLUTIONS OF ELLIPTIC AND PARABOLIC EQUATIONS , 1974 .

[18]  Andrei V. Fursikov,et al.  On exact boundary zero-controlability of two-dimensional Navier-Stokes equations , 1994 .

[19]  Lagrange principle for problems of optimal control of ill-posed or singular distributed systems , 1992 .

[20]  J. Lions.  Optimal Control of Systems Governed by Partial Differential Equations , 1971 .