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Pointwise estimates of solutions for the nonlinear viscous wave equation in even dimensions
Acta Mathematica Scientia ( IF 1 ) Pub Date : 2020-06-05 , DOI: 10.1007/s10473-020-0409-x
Nianying Li

In this article, we study the pointwise estimates of solutions to the nonlinear viscous wave equation in even dimensions ( n ≥ 4). We use the Green’s function method. Our approach is on the basis of the detailed analysis of the Green’s function of the linearized system. We show that the decay rates of the solution for the same problem are different in even dimensions and odd dimensions. It is shown that the solution exhibits a generalized Huygens principle.

中文翻译:

偶数维非线性粘性波动方程解的逐点估计

在本文中,我们研究了偶数维 (n ≥ 4) 非线性粘性波动方程解的逐点估计。我们使用格林函数法。我们的方法基于对线性化系统格林函数的详细分析。我们表明,同一问题的解的衰减率在偶数维和奇数维上是不同的。结果表明,该解具有广义惠更斯原理。
更新日期:2020-06-05
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