摘要
本文研究一类n维拟线性双曲—抛物型方程,具有非线性初边值条件的奇摄动问题,我们证明了在摄动问题光滑解存在的区域内,具有一致有效的一阶渐近展开式。我们建立了相应的能量不等式,进而导出其余项在某种模意义下的估计式:‖Z‖=O(ε)~2本文拓广了文[2]—[5]的工作。
This paper deals with singularily perturbed problem of a kind of n-dimensional uasilinear hyperbolic-parabolic type equations, subject to nonlinear intial-boundary value onditions. We make the energy inequality about this perturbed problem and prove that, the ormal asymptotic solution is asymptotic expansion of smoothing solution on its existed domaia or original perturbed problem. For the remainder Z, the estimation ‖Z‖=O(ε~2) is valid nifermly n Q. This paper deduces the result of works [2]-[5].
基金
国家自然科学基金
关键词
偏微分方程
初边值问题
奇摄动
Partial differential equation, Nonlinear initial-boundary value problem, Theory of singular perturbation
