Global Existence and Decay Properties of Solutions for Coupled Degenerate Dissipative Hyperbolic Systems of Kirchhoff Type

Access this Article

Author(s)

Abstract

Consider the initial-boundary value problem for coupled degenerate dissipative hyperbolic systems of Kirchhoff type: ρ<i>u</i><sub><i>tt</i></sub> − (||∇<i>u</i>(<i>t</i>)||<sup>2</sup> + ||∇<i>v</i>(<i>t</i>)||<sup>2</sup>)<sup>γ</sup>Δ<i>u</i> + <i>u</i><sub><i>t</i></sub> = 0, ρ<i>v</i><sub><i>tt</i></sub> − (||∇<i>u</i>(<i>t</i>)||<sup>2</sup> + ||∇<i>v</i>(<i>t</i>)||<sup>2</sup>)<sup>γ</sup>Δ<i>v</i> + <i>v</i><sub><i>t</i></sub> = 0, with homogeneous Dirichlet boundary condition and ρ > 0 and γ > 0. When either the coefficient ρ or the initial data are appropriately small, we prove the global existence theorem by using several identities and the energy decay. Moreover, under the same assumption for ρ and the initial data, we derive the decay estimates of the solutions and their second order derivatives.

Journal

  • Funkcialaj Ekvacioj

    Funkcialaj Ekvacioj 57(2), 319-337, 2014

    Division of Functional Equations, The Mathematical Society of Japan

Codes

  • NII Article ID (NAID)
    130004678001
  • Text Lang
    ENG
  • ISSN
    0532-8721
  • Data Source
    J-STAGE 
Page Top