半无界区域上算子L_q=~2/(t^2)-~2/(x^2)+q(t)的反问题

The Inverse Problem of the Operator L q= 2t 2- 2x 2+q(t) in Semi unbounded Domain

讨论半无界区域上如下双曲方程确定函数偶（ｕ，ｑ）的反问题：ｕｔ－ｕｘｘ＋ｑ（ｔ）ｕ＝Ｆ（ｘ，ｔ），ｘ＞０，ｔ＞０，ｕ（ｘ，０）＝φ（ｘ），ｕｔ（ｘ，０）＝ψ（ｘ），ｘ≥０，ｕ（０，ｔ）＝ｆ（ｔ），ｔ≥０，ｕｘ（０，ｔ）＝ｇ（ｔ），ｔ≥０．给出了局部解的存在性、唯一性和稳定性结果．

The study of the inverse problem of identifying unknown functions (u,q) is studied which satisfies the following problem:u tt -u xx +q(t)u=F(x,t),x>0,t>0, u(x,0)=φ(x),u t(x,0)=ψ(x),x≥0, u(0,t)=f(t),t≥0, u x(0,t)=g(t),t≥0.By using the method of fixed point theorem and prior estimate,the existence, uniqueness and stability of the solution are demonstrated.