In this paper we study local and global in time existence for a class of nonlinear evolution equations having order eventually greater than 2 and not integer. The linear operator has an homogeneous damping term; the nonlinearity is of polynomial type without derivatives:

$ u_{tt}+ (-\Delta)^{2\theta}u+2\mu(-\Delta)^\theta u_t + |u|^{p-1}u = 0, \quad t\geq0, \ x\in {\mathbb{R}}^n, $

中文翻译：

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半线性高阶方程的大数据解

在本文中，我们研究一阶最终大于2而不是整数的非线性演化方程的时间局部存在和全局存在。线性算子具有均匀的阻尼项。非线性是多项式类型，没有导数：

$ u_ {tt} +（-\ Delta）^ {2 \ theta} u + 2 \ mu（-\ Delta）^ \ theta u_t + | u | ^ {p-1} u = 0，\ quad t \ geq0 ，\ x \ in {\ mathbb {R}} ^ n，$