Asymptotic behavior for systems of nonlinear wave equations with multiple propagation speeds in three space dimensions

作者：Katayama Soichiro^*

来源：Journal of Differential Equations, 2013, 255(1): 120-150.

DOI：10.1016/j.jde.2013.04.003

• Nonlinear wave equation
• Multiple propagation speeds
• Null condition
• Asymptotic behavior

We consider the Cauchy problem for systems of nonlinear wave equations with multiple propagation speeds in three space dimensions. Under the null condition for such systems, the global existence of small amplitude solutions is known. In this paper, we will show that the global solution is asymptotically free in the energy sense, by obtaining the asymptotic pointwise behavior of the derivatives of the solution. Nonetheless we can also show that the pointwise behavior of the solution itself may lie quite different from that of the free solution. In connection with the above results, a theorem is also developed to characterize asymptotically free solutions for wave equations in arbitrary space dimensions.

• 出版日期2013-7-1