Weakly coupled systems of semilinear elastic waves with different damping mechanisms in 3D
Weakly coupled systems of semilinear elastic waves with different damping mechanisms in 3D
We consider the following Cauchy problem for weakly coupled systems of semi-linear damped elastic waves with a power source non-linearity in three-dimensions: \begin{equation*} U_{tt}-a^2ΔU-\big(b^2-a^2\big)\nabla\text{div } U+(-Δ)^θU_t=F(U),\,\, (t,x)\in[0,\infty)\times\mathbb{R}^3, \end{equation*} where $U=U(t,x)=\big(U^{(1)}(t,x),U^{(2)}(t,x),U^{(3)}(t,x)\big)^{\mathrm{T}}$ with $b^2>a^2>0$ and $θ\in[0,1]$. Our interests are some qualitative properties of solutions to the corresponding linear model with vanishing right-hand …