Energy estimates for hyperbolic equations in unbounded domains and their applications

首先确定了一类阻尼系数在无穷远临界衰减的半线性波动方程的能量衰减率。其次，我们得到了具有各向异性变系数的线性波动方程在外部区域的局部能量衰减性质，最后，我们得到了具有次临界势的半线性阻尼波动方程的所谓Fujita型临界指数。

Firstly we determined the decay rate of the energy for some semi-linear wave equations with a damping coefficient decaying critically near infinity. Secondly we obtained the local energy decay property in an exterior domain for the linear wave equations with anisotropic variable coefficients, and finally we found the so called Fujita type critical exponent for some semi-linear damped wave equations with a sub-critical potential.