L2(Σ)-regularity of the boundary to boundary operator B∗L for hyperbolic and Petrowski PDEs
By Irena Lasiecka, Roberto Triggiani. 2003
53 citations recorded by the source corpus.
This paper takes up and thoroughly analyzes a technical mathematical issue in PDE theory, whileas a by-pass productmaking a larger case. The technical issue is the L2(Σ)-regularity of the boundary → boundary operator B∗L for (multidimensional) hyperbolic and Petrowski-type mixed PDEs problems, where L is the boundary input → interior solution operator and B is the control operator from the boundary. Both positive and negative classes of distinctive PDE illustrations are exhibited and proved. The larger case to be made is that hard analysis PDE energy methods are the tools of the tradenot soft analysis methods. This holds true not only to analyze B∗L, but also to establish three inter-related cardinal results: optimal PDE regularity, exact controllability, and uniform stabilization. Thus, the paper takes a critical view on a spate of abstract results in infinite-dimensional systems theory, generated by unnecessarily complicated and highly limited soft methods, with no apparent awareness of the high degree of restriction of the abstract assumptions madefar from necessaryas well as on how to verify them in the case of multidimensional dynamical systems such as PDEs.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0ad2aeaeaf05ac8f2f6a1ecba10f2026bbb8fcb2
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In Computational Theory and Mathematics
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Citations in the corpus
- Infinite‐Dimensional Linear Systems: a Distributional Approach (2005, methodology): “In general, the above system will not be a well-posed linear system, nor is it included in the class of ‘abstract parabolic systems’ as studied by Lasiecka and Triggiani in [13].”