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Integral inequalities and applications to the stability of nondissipative distributed systems. (Sur des inégalités intégrales et applications à la stabilité de quelques systèmes distribués non dissipatifs.) (French. English summary) Zbl 1407.93332

Summary: First we prove some new integral inequalities to obtain a precise estimate on behavior at infinity of a positive and not necessarily decreasing function. This extends in many directions and improves in certain cases some integral inequalities due to A. Haraux, V. Komornik, P. Martinez, M. Eller et al. and F. Alabau-Boussouira concerning decreasing functions. Then we give applications to (internal or boundary, linear or nonlinear) stabilization of certain nondissipative distributed systems, which improve and generalize many stabilization results known in the dissipative case. The variety of systems considered proves that the method developed in this paper is direct and very flexible; it can be applied to various nondissipative problems and it allows one to obtain general estimates (exponential, polynomial, logarithmic or other) of stability.

MSC:

93D15 Stabilization of systems by feedback
26A12 Rate of growth of functions, orders of infinity, slowly varying functions
35B40 Asymptotic behavior of solutions to PDEs
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