Resolvent estimates for the one-dimensional damped wave equation with unbounded damping

2022/06/17 by Arnal, Antonio
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2206.08820

Abstract

We study the generator G of the one-dimensional damped wave equation with unbounded damping. We show that the norm of the corresponding resolvent operator, ‖ (G - λ)^-1 ‖, is approximately constant as |λ| → +∞ on vertical strips of bounded width contained in the closure of the left-hand side complex semi-plane, ℂ_- := \λ∈ ℂ: Re λ≤ 0\. Our proof rests on a precise asymptotic analysis of the norm of the inverse of T(λ), the quadratic operator associated with G.

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