半线性奇异双曲方程组哥西问题的整体解

On the Global Existence of Semi-linear Hyperbolic Systems with Singular Coefficients

文章在空间 L2 ( Rn)中考虑半线性奇异双曲方程组的哥西问题( S) tσdudt+Au -tρBu =f ( t,u) 0≤ t≤ Tlimt→ 0 + u( t) =0在算子 A、B及函数 f ( t,λ)的某些假设下 ,证明了问题 ( S)在函数类 C0 ( [0 ,T],L2 ( Rn) )∩ C1( ( 0 ,T) ,L2 ( Rn) )中整体解存在 .

In this paper, we study the following Cauchy probrem (S)t σdudt+Au-t ρBu=f(t,u) 0<t≤T lim t→0 +u(t)=0 in the space L 2(1R n). When operator A,B and function f(t,λ) satisfy certain conditions, we have proved the global existence of solutions of (S) in the functions of class C 0([0,T],L 2)∩C 1((0,T],L 2) .