Asymptotic Solutions of Initial-Boundary Value Problems for Wave Equations with a Small Parameter
Some initial-boundary value problems for wave equations with a small parameter are studied.The problem whose approximate solution is constructed using the method of multiple scales.An as-ymptotic expansion is obtained,which is considered to be uniformly valid,by introducing different time scales in perturbed expansion and progressively eliminating secular terms from appearing in each order expansion.And then a precise analysis of the above uniformly validity is given using the theory of asymptotic expansion.The result is shown to regard a first order uniform expansion as an approxi-mate solution of this problem,in agreement with whose exact solution to O(ε2).
wave equationsinitial-boundary value problemsasymptotic solutionsthe method of mul-tiple scalesUniformly validity
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