THE POINT-WISE ESTIMATES FOR THE SOLUTION OF DAMPED WAVE EQUATION WITH NONLINEAR CONVECTION IN MULTI-DIMENSIONAL SPACE

摘要

In this paper, we study the time-asymptotic behavior of the solution for the Cauchy problem of the damped wave equation with a nonlinear convection term in the multi-dimensional space. When the initial data is a small perturbation around a constant state u~*, we obtain the point-wise decay estimates of the solution under the so-called dissipative condition |b| ? 1, where b depends on u~* and the nonlinear term.