scholarly journals On decay properties of solutions for degenerate strongly damped wave equations of Kirchhoff type

2011 ◽  
Vol 381 (1) ◽  
pp. 229-239 ◽  
Author(s):  
Kosuke Ono
Keyword(s):  
Wave Equations ◽  
Kirchhoff Type ◽  
Decay Properties ◽  
Strongly Damped

scholarly journals On the existence of solutions of strongly damped nonlinear wave equations

2000 ◽  
Vol 23 (6) ◽  
pp. 369-382 ◽  
Author(s):  
Jong Yeoul Park ◽  
Jeong Ja Bae
Keyword(s):  
Nonlinear Wave ◽  
Existence And Uniqueness ◽  
Wave Equations ◽  
Existence Of Solutions ◽  
Hyperbolic Type ◽  
Nonlinear Wave Equations ◽  
Gamma Delta ◽  
Uniqueness Of Solutions ◽  
Alpha Beta ◽  
Strongly Damped

We investigate the existence and uniqueness of solutions of the following equation of hyperbolic type with a strong dissipation:utt(t,x)−(α+β(∫Ω|∇u(t,y)|2dy)γ)Δu(t,x)                                −λΔut(t,x)+μ|u(t,x)|q−1u(t,x)=0,     x∈Ω,t≥0            u(0,x)=u0(x),          ut(0,x)=u1(x),      x∈Ω,  u|∂Ω=0, whereq>1,λ>0,μ∈ℝ,α,β≥0,α+β>0, andΔis the Laplacian inℝN.

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