非线性边界条件下的线性波动方程的解

Solutions to a linear wave equation with nonlinear boundary conditions

讨论一维线性波动方程和非线性边界条件的关系.证明了一类一维线性波动方程在非线性边界条件下,存在唯一的局部解.同时也证明了由于边界条件的非线性,初始值只要满足一定的条件,即使很小,对应的解也会在有限时间内爆破.在证明过程中,同时给出了爆破时间的上界.

This paper was concerned with associated with nonlinear boundary conditions a one-dimensional The unique local linear wave equation solution to the wave equation was proved to exist. The result is that the nonlinearity at the boundary causes a finite time blow up of the solution, even for small initial data. And the upper bound to the blow up time is given in the paper.