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关于一类双曲型方程初—边值问题解法探讨

ON THE SOLUTION METHOD OF INITIAL-BOUNDARY PROBLEM FOR HYPERBOLIC EQUATIONS
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摘要 研究一维波动方程的初一边值问题,通常用分离变量法。作者探索把初一边值问题中的初始函数在相应的本征函数族下展开成为Fourier级数,把初始函数延拓到整个数轴,把初一边值问题的求解转化成初值问题的求解,从而使这两类不同的定解问题的求解方法统一起来。 To study initial - boundary value problems for hyperbolic equations, usuallythe method of separation of variables may be used. The writers try to expand theinitial function among the initial - boundary value problems in a Fourier seriesunder relevant eigenfunction system and reduce the solving of the initial-boundaryvalue problems to the solving of the initial value problem by the continuationof the initial function outside the given interval, thus integrating the two dif-ferent methods to solve problems.
出处 《大庆石油学院学报》 CAS 北大核心 1989年第3期94-99,共6页 Journal of Daqing Petroleum Institute
关键词 双曲型方程 初一边值 偏微分方程 eigenvalue eigenfunction characteristic curves superposition extention uniform convergence
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