Title page for etd-0627114-234123


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URN etd-0627114-234123
Author Che-wei Tsao
Author's Email Address m022040009@student.nsysu.edu.tw
Statistics This thesis had been viewed 5559 times. Download 658 times.
Department Applied Mathematics
Year 2013
Semester 2
Degree Master
Type of Document
Language English
Title Nodal and blow-up problems related to some evolution equations
Date of Defense 2014-07-25
Page Count 61
Keyword
  • uniform estimate
  • blow-up rate
  • nonlinear heat equation
  • nodal points
  • Stieltjes string
  • Abstract In this thesis, we study two different evolutionary problem. The first one is the nodal point position of the Stieltjes string, which is a discrete version of the vibrating strings after separation of variables. We can express the nodal positions of some special solutions in terms of a continued fraction involving the given data (masses and lengths between masses) of the problem. The solutions are associated with the maximal eigenvalues for Dirichlet-Dirichlet problem and Dirichlet-Neumann problem. Our result is new in literature.
       Another problem is about the profile of the blow-up solution of some nonlinear heat
    equation,
       u_t − Δu = |u|^(p−1) u    (x, t) ∈ Ω × (0, T),
    with initial boundary conditions u(x, 0) = u0(x) and u(x, t) = 0 when (x, t) ∈ ∂Ω × (0, T), where Ω is a bounded convex domain. Using a sophisticated scaling method, Giga-Kohn (1989) gave a uniform estimate of this blow-up solution. We shall follow B. Hu’s book to give a clear exposition to this result, giving more details in the long
    proof. We also show in detail that the uniform estimate result still holds when Ω = R^n, which is unbounded. We hope that this account will be useful for beginning graduate students to understand the method. It is believed that the method is important in the development of the subject.
    Advisory Committee
  • Hsin-Yuan Huang - chair
  • Tsung-Lin Lee - co-chair
  • Chi Cheung Poon - co-chair
  • Chun-Kong Law - advisor
  • Files
  • etd-0627114-234123.pdf
  • Indicate in-campus at 2 year and off-campus access at 2 year.
    Date of Submission 2014-07-29

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