English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this work, we consider a system of two wave equations coupled byvelocities in one-dimensional space, with one boundary fractional damping.First, we show that the system is strongly asymptotically stable if and only ifthe coupling parameter b of the two equations is outside a discrete set ofexceptional real values. Next, we show that our system is not uniformly stable.Hence, we look for a polynomial decay rate for smooth initial data. Usingfrequency domain approach combining with multiplier method, we prove that theenergy decay rate is greatly influenced by the nature of the coupling parameterb, the arithmetic property of the ratio of the wave propagation speeds a, theorder of the fractional damping. Indeed, under the equal speed propagationcondition, we establish an optimal polynomial energy decay rate. Furthermore,when the wave propagate with different speeds, under some arithmetic conditionson the ratio of the wave propagation speeds, we prove that the energy of oursystem decays polynomially to zero.

The influence of the coefficients of a system of coupled wave equations with fractional damping on its stabilization