一类非线性波动方程整体解的存在性

Existence of global solution to a nonlinear wave equation

利用形式常微分方程和半群理论对一类带有阻尼项和力源项的非线性波动方程进行了研究,得到当方程的非线性项满足Lipschitz连续及连续可微条件时方程在有界区域上的经典解存在,并且进一步获得了方程整体解在无界区域上存在且唯一的结论.

In this paper, we studied the Cauchy problem for a nonlinear wave equation with nonlinear damping and source terms which using abstract ODE and semigroup theory. Under the nonlinear term satisfied Lipschitz continuous and continuously differentiable, we proved the existence of the classical solution on bound domains, and then established the global well -posedness in unbound domains.