Large Time Behavior of Solutions to Burgers Equation with a Time Delay

Abstract

In this article, we consider the large time behavior of solutions $ρ$ to the one-dimensional Cauchy problem of the generalized viscous Burgers equations with a time delay. More precisely, we derive the time decay estimate of the solution to the Cauchy problem, provided by $ρ_0(0)∈L^1$ and $ρ_0∈C([−τ,0];H^1 ).$ The result is based on the combination of the weighted $L^2$ energy estimate and the $L^1$ estimate.