This article is cited in 4 papers

Problems of two-sided boundary control for the wave equation on subcritical intervals in classes of strong generalized solutions

M. M. Potapov, D. A. Ivanov

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: Problems with two-sided boundary controls of three main types are considered for the wave equation with variables coefficients. Constructive inequalities for the bounded invertibility of the control operator with known (computable) values of estimate constants are obtained in classes of strong generalized solutions on intervals of subcritical length. The obtained estimates make it possible to use the variational method for finding stable numerical solutions to the problems under consideration on time intervals of any subcritical or exactly critical length.

Keywords: wave equation, boundary control, subcritical interval, bounded invertibility inequality, variational method.

UDC: 517.956.37

Received: 22.01.2013

 English version: Proceedings of the Steklov Institute of Mathematics (Supplement Issues), 2014, 287, suppl. 1, S145–S155

Bibliographic databases:

• 
• 
• 
•