MR3241908
Kosuke ONO
Kosuke ONO
Global Existence and Decay Properties of Solutions for Coupled Degenerate Dissipative Hyperbolic Systems of Kirchhoff Type
Funkcialaj Ekvacioj. Serio Internacia
57
2014
319--337
http://fe.math.kobe-u.ac.jp/FE/FullPapers/57-2/57_319.pdf
http://www.ams.org/mathscinet-getitem?mr=MR3241908
Consider the initial-boundary value problem for coupled degenerate dissipative hyperbolic systems of Kirchhoff type: $\rho u_{tt}-\left(\|\nabla u(t)\|^2+\|\nabla v(t)\|^2\right)^\gamma\Delta u+u_t=0$, $\rho v_{tt}-\left(\|\nabla u(t)\|^2+\|\nabla v(t)\|^2\right)^\gamma\Delta v+v_t=0$, with homogeneous Dirichlet boundary condition and $\rho>0$ and $\gamma>0$. When either the coefficient $\rho$ 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 $\rho$ and the initial data, we derive the decay estimates of the solutions and their second order derivatives.
Dissipative wave equation, Degenerate, Kirchhoff type, Decay estimates.
35L52, 35B40.
57-319
2014
Global Existence and Decay Properties of Solutions for Coupled Degenerate Dissipative Hyperbolic Systems of Kirchhoff Type
Kosuke ONO
Kosuke ONO
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