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Riesz Basis Generation of Abstract Second-Order Partial Differential Equation Systems with General Non-Separated Boundary Conditions |
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| Authors: | Bao-Zhu Guo Jun-Min Wang |
| Affiliation: | 1. Academy of Mathematics and Systems Science, Academia Sinica , Beijing , People's Republic of China;2. School of Computational and Applied Mathematics , University of the Witwatersrand , Johannesburg , South Africa bzguo@iss.ac.cn;4. Department of Mathematics , Beijing Institute of Technology , Beijing , People's Republic of China;5. School of Computational and Applied Mathematics , University of the Witwatersrand , Johannesburg , South Africa |
| Abstract: | Riesz basis analysis for a class of general second-order partial differential equation systems with nonseparated boundary conditions is conducted. Using the modern spectral analysis approach for parameterized ordinary differential operators, it is shown that the Riesz basis property holds for the general system if its associated characteristic equation is strongly regular. The Riesz basis property can then be readily established in a unified manner for many one-dimensional second-order systems such as linear string and beam equations with collocated or noncollocated boundary feedbacks and tip mass attached systems. Three demonstrative examples are presented. |
| Keywords: | Partial differential equation Riesz basis Spectral operator Vibrating system |