论文标题
衰减估计和炸毁一类热方程的解决方案
Decay estimates and blow up of solutions to a class of heat equations
论文作者
论文摘要
在本文中，我们研究了具有多项式和对数函数的乘积的非线性的半线性热方程。使用潜在井的不变性，我们已经建立了$ l^2 $ - 规范解决方案的全局存在和指数衰减估计，而没有在适当条件下对初始数据的适当条件中的指数限制。此外，还讨论了亚临界，关键和超临界初始能级的有限时间。
In this article, we study a semi-linear heat equation with the nonlinearity which is the product of polynomial and logarithmic functions. Using the invariance of the potential well(s), we have established the global existence and exponential decay estimates of solutions in $L^2$ - norm without having any restriction on the exponent in the source term under suitable conditions on the initial data. Moreover, finite time blow up of solutions at subcritical, critical and supercritical initial energy levels is also discussed.
