DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Kim, Yong-Jung | - |
dc.contributor.advisor | 김용정 | - |
dc.contributor.author | Kim, Kyung-Lim | - |
dc.contributor.author | 김경림 | - |
dc.date.accessioned | 2011-12-14T04:56:46Z | - |
dc.date.available | 2011-12-14T04:56:46Z | - |
dc.date.issued | 2009 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=327296&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/42219 | - |
dc.description | 학위논문(석사) - 한국과학기술원 : 수리과학과, 2009. 8., [ v, 30 p. ] | - |
dc.description.abstract | In this paper, an asymptotic approximate solution to the Burgers equation is constructed. The heat equation with nonnegative initial value has a linear combination of $n$ heat kernels as an approximate solution with convergence order $O(t^{\frac{1}{2r} - \frac{2n+1}{2}})$ in $L^r$ -norm, $1 \leq r \leq \infin$, as $t \rightarrow \infin$. The Burgers equation is obtained by adding a nonlinear convective term to the heat equation, and in turn one may question whether a similar form of the approximate solution exists. Note that, the Cole-Hopf transformation transforms a solution of nonlinear Burgers equation into the solution of the linear heat equation. Using Cole-Hopf transformation, we obtain an approximate solution to the Burgers equation by inverse-transforming a linear combination of $n$ heat kernels. Surprisingly, the algebraic convergence order of the Burgers equation is preserved, having $O(t^{\frac{1}{2r} - \frac{2n+1}{2}})$ in $L^r$ -norm, $1 \leq r \leq \infty$, as $t \rightarrow \infty$. Furthermore, we expect that the moments of the solution to the Burgers equation and those of approximate solution coincide at $t = \infty$. Some numerical results are included to show the convergence order. | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | Burgers | - |
dc.subject | moment | - |
dc.subject | asymptotics | - |
dc.subject | convergence | - |
dc.subject | 버거스 | - |
dc.subject | 모멘트 | - |
dc.subject | 근사 | - |
dc.subject | 수렴 | - |
dc.subject | Burgers | - |
dc.subject | moment | - |
dc.subject | asymptotics | - |
dc.subject | convergence | - |
dc.subject | 버거스 | - |
dc.subject | 모멘트 | - |
dc.subject | 근사 | - |
dc.subject | 수렴 | - |
dc.title | Control of moments at $t = \infin$ and higher order asymptotics in the burgers equation | - |
dc.title.alternative | 무한시간에서의 모멘트 조절을 통한 버거스 해의 근사 | - |
dc.type | Thesis(Master) | - |
dc.identifier.CNRN | 327296/325007 | - |
dc.description.department | 한국과학기술원 : 수리과학과, | - |
dc.identifier.uid | 020083045 | - |
dc.contributor.localauthor | Kim, Yong-Jung | - |
dc.contributor.localauthor | 김용정 | - |
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