Exponential decay of the viscoelastic wave equation of Kirchhoff type with a nonlocal dissipation
DOI:
https://doi.org/10.24193/subbmath.2020.3.10Keywords:
Kirchhoff equation, nonlocal damping, global solution, energy decay, relaxation function.Abstract
The following viscoelastic wave equation of Kirchhoff type with non- linear and nonlocal damping
utt − ψ (I I2\ 2 ∆u − α∆ut t + g(t − τ )∆u(τ )dτ + M 0 (I∇uI2\ u = f (u),
where M (r) is a C1([0, ∞)) -function satisfying M (r) ≥ m1 > 0 for r ≥ 0, is considered in a bounded domain Ω of RN . The existence of global solutions and decay rates of the energy are proved.
Mathematics Subject Classification (2010): 35L05, 35L70, 93D15.
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