One-dimensional damped wave equation with large initial perturbation (Q2854021)

Considered is an initial-boundary value problem for the damped wave equation with a nonlinear convection term in the half line. The purpose of the paper is to show some new results on the global stability of weak boundary layer solutions to the stated problem. The considered problem is reformulated by introducing the boundary layer solution in the model. The local solvability of the reformulated problem is then transferred to the local solvability of an integral-differential equation. Further, for a class of large initial perturbations, it is proved that under some specific assumptions, the problem admits a unique global solution which converges to the boundary layer solution uniformly, as time tends to infinity. Algebraic convergence rates for the constructed solution as well as exponential decay rates are shown.