Fractional semilinear damped wave equation on the Heisenberg group
Fractional semilinear damped wave equation on the Heisenberg group
This paper aims to investigate the Cauchy problem for the semilinear damped wave equation for the fractional sub-Laplacian $(-\mathcal{L}_{\mathbb{H}})^{\alpha}$, $\alpha>0$ on the Heisenberg group $\mathbb{H}^{n}$ with power type non-linearity. With the presence of a positive damping term and nonnegative mass term, we derive $L^2-L^2$ decay estimates for the solution of …