关键词: 奇摄动, 积分微分方程, 双曲型方程

Abstract: We considered a class of generalized two parameter nonlinear hyperbolic  integraldifferential equation with singular perturbation model. Firstly, the generalized outer solution of the model was obtained by using the generalized Fredholm type integral equation. Secondly, the boundary layer corrective term of the generalized solution was obtained by using the method of multiple scale variables. Thirdly, the initial layer corrective term of the generalized solution was obtained by using the stretched variable method. Finally, the synthetic asymptotic expansion of the generalized singular perturbation solution was constructed, and the uniform validity of the asymptotic expansion of the solution was proved by using the fixed point theory.

Key words: hyperbolic equation, integraldifferential equation, singular perturbation