非线性摄动电报方程初值问题的渐近理论

THE ASYMPTOTIC THEORY OF SOLUTIONS OFINITIAL VALUE PROBLEMS FOR NONLINEARPERTURBED TELEGRAPH EQUATIONS

对一类二阶半线性摄动电报方程，给出了一个渐近方法，证明了解的渐近理论及形式近似解的合理性都在时间变量无穷大时（０≤ｔ≤Ｏ（｜ε｜－１））成立，并推广了赖绍永的工作［应用数学及力学，１９９７，１８（７）：６１１～６１６］．

The asymptotic theory and the validation of the formal approximations for a second order semilinear perturbed telegraph equation are studied on the timescale of order O(|ε|-1)(0≤t≤O(|ε|-1)). Some known results of Lai Shaoyong [Applied Mathematics and Mechanics,1997,18(7):611～616] are generalized.