Structurally damped $\sigma -$evolution equations with power-law memory

Nelson Faustino, Jorge Marques

We consider an integro-differential counterpart of the $\sigma -$evolution equation of the type \[ \partial_t^2 u(t,x)+μ(-Δ)^{\fracσ{2}} \partial_t u(t,x)+(-Δ)^σu(t,x)=f(t,x), \] with $σ…