Global asymptotics of solutions to the Cauchy problem for the damped wave equation with absorption

Abstract

We consider the Cauchy problem for the damped wave equation with absorption{A formula is presented} The behavior of u as t → ∞ is expected to be same as that for the corresponding heat equation φ{symbol}t - Δ φ{symbol} + | φ{symbol} |ρ - 1 φ{symbol} = 0, ( t, x ) ∈ R+ × RN. In the subcritical case 1 < ρ