On the Asymptotic Stability of Wave Equations Coupled by Velocities of Anti-symmetric Type

【Author】

Yan CUI;Zhiqiang WANG;Department of Mathematics, Jinan University;School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics,Fudan University;

【Institution】

Department of Mathematics, Jinan University;School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics,Fudan University;

【Abstract】

In this paper, the authors study the asymptotic stability of two wave equations coupled by velocities of anti-symmetric type via only one damping. They adopt the frequency domain method to prove that the system with smooth initial data is logarithmically stable, provided that the coupling domain and the damping domain intersect each other.Moreover, they show, by an example, that this geometric assumption of the intersection is necessary for 1-D case.

【Keywords】

Wave equations;;Coupled by velocities;;Logarithmic stability

References

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Springer Journals Database

Total: 13 articles

  • [1] Nicolas Burq, Décroissance de l'énergie locale de l'équation des ondes pour le problème extérieur et absence de résonance au voisinage du réel, Acta Mathematica,
  • [2] Exponential Decay of Solutions to Hyperbolic Equations in Bounded Domains, Indiana University Mathematics Journal,
  • [3] Nicolas Burq;;Michael Hitrik, Energy decay for damped wave equations on partially rectangular domains, Mathematical Research Letters,
  • [4] Xiaoyu Fu, Logarithmic Decay of Hyperbolic Equations with Arbitrary Small Boundary Damping, Communications in Partial Differential Equations,

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