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Asymmetric invariants for a class of strictly hyperbolic systems including the Timoshenko beam
Author(s) -
Marchionna Clelia,
Panizzi Stefano
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.842
Subject(s) - mathematics , conservation law , mathematical analysis , perturbation (astronomy) , dimension (graph theory) , hyperbolic partial differential equation , quadratic equation , class (philosophy) , space (punctuation) , pure mathematics , partial differential equation , geometry , linguistics , philosophy , physics , quantum mechanics , artificial intelligence , computer science
We introduce a set of conserved quantities of energy‐type for a strictly hyperbolic system of two coupled wave equations in one space dimension. The system is subject to mechanical boundary conditions. Some of these invariants are asymmetric in the sense that their defining quadratic form contains second order derivatives in only one of the unknowns. We study their independence with respect to the usual energies and characterize their sign. In many cases, our results provide sharp well‐posedness and stability results. Finally, we apply some of our conservation laws to the study of a singular perturbation problem previously considered by J. Lagnese and J. L. Lions. Copyright © 2007 John Wiley & Sons, Ltd.