Linear and Nonlinear Hyperbolic Equations

Observability estimates for 1-D wave equations with non-Lipschitz coefficients

speaker: Francesco Fanelli (Institut Camille Jordan - UMR CNRS 5208, Universite Claude Bernard - Lyon 1)

abstract: In this talk we will deal with the control problem for the 1-D wave equation

(1) ω(x) ∂2t u - ∂2x u = 0

on the interval [0,1], under minimal regularity assumptions over the coefficient ω In a first time, we will show “classical” observability estimates for ω satisfying an integral Zygmund condition. In particular, this result represents an improvement to the previous one for BV coefficients. Then we will consider lower regularity hypothesis: for ω log-Lipschitz or log-Zygmund, we will prove observability estimates “with a finite loss of derivatives”. Finally, we will discuss the sharpness of our results.

timetable:
Tue 2 Jul, 15:30 - 16:00, Aula Dini
documents:

Abstract

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