• Title, Summary, Keyword: inertial manifold

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AN EXISTENCE OF THE INERTIAL MANIFOLD FOR NEW DOMAINS

  • Kwean, Hyuk-Jin
    • Journal of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.693-707
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    • 1996
  • Consider a specific class of scalar-valued reaction diffusion equations of the form $$ (1.1) u_t = \nu\Delta u + f(u), u \in R $$ where $\nu$ < 0 is viscosity parameter and $f : R \to R$ is sufficiently smooth.

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NEGATIVELY BOUNDED SOLUTIONS FOR A PARABOLIC PARTIAL DIFFERENTIAL EQUATION

  • FANG ZHONG BO;KWAK, MIN-KYU
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.4
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    • pp.829-836
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    • 2005
  • In this note, we introduce a new proof of the unique-ness and existence of a negatively bounded solution for a parabolic partial differential equation. The uniqueness in particular implies the finiteness of the Fourier spanning dimension of the global attractor and the existence allows a construction of an inertial manifold.

A GEOMETRIC CRITERION FOR THE WEAKER PRINCIPLE OF SPATIAL AVERAGING

  • Kwean, Hyuk-Jin
    • Communications of the Korean Mathematical Society
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    • v.14 no.2
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    • pp.337-352
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    • 1999
  • In this paper we find a geometric condition for the weaker principle of spatial averaging (PSA) for a class of polyhedral domains. Let \ulcorner be a polyhedron in R\ulcorner, n$\leq$3. If all dihedral angles of \ulcorner are submultiples of $\pi$, then there exists a parallelopiped \ulcorner generated by n linearily independent vectors {\ulcorner}\ulcorner in R\ulcorner containing \ulcorner so that solutions of $\Delta$u+λu=0 in \ulcorner with either the boundary condition u=0 or ∂u/∂n=0 are expressed by linear combinations of those of $\Delta$u+λn=0 in \ulcorner with periodic boundary condition. Moreover, if {\ulcorner}\ulcorner satisfies rational condition, we guarantee the weaker PSA for the domain \ulcorner.

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A Study on the Structural Integrity Considering the Installation of a Micro-tube Heat Exchanger (미세튜브 열교환기의 장착을 고려한 구조건전성에 관한 연구)

  • Oh, Se Yun;Kim, Tae Jin;Cho, Jong Rae;Jeong, Ho Sung
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.39 no.4
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    • pp.447-451
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    • 2015
  • The objective of this study is to predict the structural characteristics of a heat exchanger mounted on an aircraft engine using finite element analysis. The plastic fracture and life of the heat exchanger were estimated by a thermo-mechanical analysis. Tensile tests were conducted under high temperature conditions (700, 800, 900, 1000 K) using five specimens to obtain the mechanical properties of the Inconel 625 tubes. To assess the structural characteristics of the heat exchanger, the full and partial models were applied under the operating conditions given by the thermo-mechanical and inertial load. As a result, the case, tubesheet, flange, and mounting components have a reasonable safety margin to the allowable stress assuming a fatigue strength of Inconel 625 of 10000 cycles under 1000 K.