带有非线性耗散项的非线性波方程弱解的存在性

Existence of Weak Solutions to the Nonlinear Wave Equations with Nonlinear Dissipations Terms

证明带有非线性耗散项ρ(x,ut)=|ut|rut的非线性波方程utt-△u+ρ(x,ut)=f(x,u)弱解的存在性,文章将利用迦辽金方法和Sobolev嵌入定理来证明.

To describepaper the existence of weak solutions to the nonlinear wave equa tions utt-△u＋ρ（x,ut）=f（x,u） with nonlinear dissipations like ρ（x,ut）=｜ut｜rut, we will use Faedo-Galekin mathodand Sobolev embedding theorem to prove this conclusion.