带粘性的波动方程组解的逐点估计

Pointwise Estimates for Systems of Wave Equations with Viscosity

论文研究了三维空间中带粘性项波动方程组解的逐点估计.同时考虑了两种非线性项:具有散度形式的非线性项和具有拉普拉斯形式的非线性项.利用长波和短波分解法,结合能量法和格林函数,得到大时间渐近形态解的逐点估计,并证实解的逐点估计可被相应具有不同传播速度(c1≠c2)的广义惠更斯波控制.同时,还得到了p≥1时最优的L^p衰减率.

The Cauchy problem for two systems of wave equations with viscosity in dimension three is considered.By using the long wave and short wave decomposition method together with energy method and Green function,the pointwise estimates of the time-asymptotic shape of the solution are given,which exhibit two kinds of generalized Huygens’waves.As a byproduct,the optimal L^p-decay rates with p≥1 of the solutions of these systems are also established.