论文标题
具有阻尼和潜在项的非线性波方程的关键指数
Critical exponent for nonlinear wave equations with damping and potential terms
论文作者
论文摘要
本文的目的是通过假设这些术语满足特殊关系来确定具有阻尼和量表不变顺序的潜在条款的非线性波方程的关键指数。我们强调的是，对于相关方程，我们的关键指数与一个相关方程（例如非线性波方程）不同，而没有较低的阶段，仅具有阻尼项，并且仅具有潜在项。此外，我们研究了空间无穷大的初始数据衰减顺序的影响。实际上，我们证明，不仅较低的术语，而且初始数据的顺序都会影响临界指数，以及解决方案最大存在时间的尖锐上限和下限。
The aim of this paper is to determine the critical exponent for the nonlinear wave equations with damping and potential terms of the scale invariant order, by assuming that these terms satisfy a special relation. We underline that our critical exponent is different from the one for related equations such as the nonlinear wave equation without lower order terms, only with a damping term, and only with a potential term. Moreover, we study the effect of the decaying order of initial data at spatial infinity. In fact, we prove that not only the lower order terms but also the order of the initial data affects the critical exponent, as well as the sharp upper and lower bounds of the maximal existence time of the solution.
