Development of singularities for a single quasi-linear equation and uniqueness of its generalized solutions준 선형 미분 방정식의 해에 대한 특이점의 전개와 초 함수 해의 유일성

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Physically, the solution of the quasi-linear equation $\{u_t+f(u)_x=0$, x∈R, t>0 $u(x,0)=u_0(x)$, x∈R$, has discontinuities after a finite time. We find the maximum time T for which its solution is smooth in R x (0,T) when the initial data are smooth and then show that the solution must have discontinuities after the time T. Next we compute, by using a numerical scheme, the development of its discontinuities. Moreover, we show the uniqueness of its generalized solution when the flux f depends not only on u but on x and t.
Advisors
Kwon, Kil-Hyunresearcher권길현researcher
Description
한국과학기술원 : 응용수학과,
Publisher
한국과학기술원
Issue Date
1989
Identifier
66609/325007 / 000871260
Language
eng
Description

학위논문(석사) - 한국과학기술원 : 응용수학과, 1989.2, [ [ii], 33 p. ]

URI
http://hdl.handle.net/10203/42324
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=66609&flag=dissertation
Appears in Collection
MA-Theses_Master(석사논문)
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