BEHAVIOR OF SOLUTIONS FOR RADIALLY SYMMETRIC SOLUTIONS FOR BURGERS EQUATION WITH A BOUNDARY CORRESPONDING TO THE RAREFACTION WAVE

Pub Date : 2016-07-01 DOI:10.18910/58900
Itsuko Hashimoto
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引用次数: 6

Abstract

Abstract We investigate the large-time behavior of the radially symm etric solution for Burgers equation on the exterior of a small ball in multi-dim ensional space, where the boundary data and the data at the far field are prescribed. In a previous paper [1], we showed that, for the case in which the boundary data is equal to 0 or negative, the asymptotic stability is the same as that for the vis cou conservation law. In the present paper, it is proved that if the boundary data is po sitive, the asymptotic state is a superposition of the stationary wave and the raref action wave, which is a new wave phenomenon. The proof is given using a standard L2 energy method and the characteristic curve method.
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边界对应于稀疏波的burgers方程径向对称解的解的性质
摘要研究了多维空间中具有边界数据和远场数据的小球表面的Burgers方程径向对称解的大时变行为。在之前的一篇论文中,我们证明了在边界数据等于0或为负的情况下,渐近稳定性与vis守恒律的渐近稳定性是相同的。本文证明了当边界数据为正时,渐近状态是驻波和稀薄作用波的叠加,是一种新的波现象。用标准的L2能量法和特征曲线法给出了证明。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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