Schrˋdinger equations in noncylindrical domains: exact controllability

作者：G O Antunes; M D G da Silva; R F Apolaya

来源：International Journal of Mathematics and Mathematical Sciences, 2006, 2006: 1-29.

DOI：10.1155/ijmms/2006/78192

We consider an open bounded set %26#x03A9;%26#x2282;%26#x211D;n and a family {K(t)}t%26#x2265;0 of orthogonal matrices of %26#x211D;n. Set %26#x03A9;t={x%26#x2208;%26#x211D;n;x=K(t)y,for all%26#x2002;y%26#x2208;%26#x03A9;}, whose boundary is %26#x0393;t. We denote by Q%26#x005E; the noncylindrical domain given by Q%26#x005E;=%26#x222A;0%26#x003C;t%26#x003C;T{%26#x03A9;t%26#x00D7;{t}}, with the regular lateral boundary %26#x03A3;%26#x005E;=%26#x222A;0%26#x003C;t%26#x003C;T{%26#x0393;t%26#x00D7;{t}}. In this paper we investigate the boundary exact controllability for the linear Schr%26#246;dinger equation u%26#x2032;%26#x2212;i%26#x0394;u=f in Q%26#x005E;(i2=%26#x2212;1), u=w on %26#x03A3;%26#x005E;, u(x,0)=u0(x) in %26#x03A9;0, where w is the control.