Null-controllability of a Hyperbolic Equation as Singular Limit of Parabolic Ones

作者：Micu Sorin^*; Ortega Jaime H; Pazoto Ademir F

来源：Journal of Fourier Analysis and Applications, 2011, 17(5): 991-1007.

DOI：10.1007/s00041-010-9168-8

• Null-controllability
• Fourier expansion
• Moment problem
• Biorthogonal
• Parabolic and hyperbolic equations

This article considers a hyperbolic equation perturbed by a vanishing viscosity term depending on a small parameter epsilon > 0. We show that the resulting parabolic equation is null-controllable. Moreover, we provide uniform estimates, with respect to epsilon, for the parabolic controls and we prove their convergence to a control of the limit hyperbolic equation. The method we use is based on Fourier expansion of solutions and the analysis of a biorthogonal sequence to a family of complex exponential functions.

• 出版日期2011-10