On asymptotic behavior of solution to a nonlinear wave equation with Spacetime speed of propagation and damping terms
DOI:
https://doi.org/10.22199/issn.0717627943574415Keywords:
Spacetime speed of propagation, Spacetime dependent damping, Asymptotic behavior, Weighted energy methodAbstract
In this paper, we consider the asymptotic behavior of solution to the nonlinear damped wave equation
u_{tt} – div(a(t, x)∇u) + b(t, x)u_{t} = −u^{p}^{−}^{1}u t ∈ [0, ∞), x ∈ R^{n}
u(0, x) = u_{0}(x), u_{t}(0, x) = u_{1}(x) x ∈ R^{n}
with spacetime speed of propagation and damping potential. We obtained L^{2} decay estimates via the weighted energy method and under certain suitable assumptions on the functions a(t, x) and b(t, x). The technique follows that of Lin et al.[8] with modification to the region of consideration in R^{n}. These decay result extends the results in the literature.
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