一类拟线性波动方程的初边值问题

Initial Boundary Value Problem for a Quasi-linear Wave Equation

考虑一类拟线性波动方程的初边值问题,利用Galerkin方法和位势井方法讨论在混合边界条件下,在非线性 阻尼与非线性源项相互干扰的情况下,强耗散与非线性因素之间的相互作用,分别得到了大初值和小初值能量情 况下该问题整体广义解的存在性,惟一性及衰减性.

The initial boundary value problem for a quasi-linear wave equation is studied. By virtue of the Galerkin approximation scheme combined with the potential well method, it is proved that under the mixed nonhomogeneous condition and the interference between nonlinear damping and source terms,the problem admits a global generalized solution which decays to zero as t → ∞.