中文摘要：

研究了具有非线性项│u│^αu的半线性波动方程的Cauchy问题，利用仿积分解及交换子估计等技术，证明了当α为一般的实数且满足一定的限制时，Cauchy问题自相似解的存在性．本文的结果回答了Planchon在其工作中所遗留的问题．

英文摘要：

We study the self-similar solution of semi-linear wave equation with powerlike nonlinearity │u│^αu. The global existence of self-similar solution has been obtained when α is a generic positive real number （with suitable restrictions） by using the paraproduct decomposition. This is a problem left open by Planchon in his previous work.