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RISS 인기검색어
- 검색키워드
- 저자 : Roger TEMAM (검색결과 3 건)
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Recent progresses in boundary layer theory
Temam, Roger,Jung, Chang-Yeol,Gie, Gung-Min Discrete and Continuous Dynamical Systems 2016 Discrete and continuous dynamical systems Vol.36 No.5
<P>In this article, we review recent progresses in boundary layer analysis of some singular perturbation problems. Using the techniques of differential geometry, an asymptotic expansion of reaction-diffusion or heat equations in a domain with curved boundary is constructed and validated in some suitable functional spaces. In addition, we investigate the effect of curvature as well as that of an ill-prepared initial data. Concerning convection-diffusion equations, the asymptotic behavior of their solutions is difficult and delicate to analyze because it largely depends on the characteristics of the corresponding limit problems, which are first order hyperbolic differential equations. Thus, the boundary layer analysis is performed on relatively simpler domains, typically intervals, rectangles, or circles. We consider also the interior transition layers at the turning point characteristics in an interval domain and classical (ordinary), characteristic (parabolic) and corner (elliptic) boundary layers in a rectangular domain using the technique of correctors and the tools of functional analysis. The validity of our asymptotic expansions is also established in suitable spaces.</P>
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FINITE VOLUME METHODS FOR CONVECTIONDOMINATED PROBLEMS
Chang-Yeol JUNG,Roger TEMAM 한국산업응용수학회 2009 한국산업응용수학회 학술대회 논문집 Vol.2009 No.5
In this work, we present a novel method to approximate stiff problems using a finite volume(FV) discretization. The stiffness is caused by the existence of a small parameter in the equation which introduces a boundary layer. The semi-analytic method consists in adding in the finite volume space the boundary layer corrector which encompasses the singularities of the problem. We verify the stability and convergence of our finite volume schemes which take into account the boundary layer structures. A major feature of the proposed scheme is that it produces an efficient stable second order scheme to be compared with the usual stable upwind schemes of order one or the usual costly second order schemes demanding fine meshes.
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Boundary layer analysis of nonlinear reaction-diffusion equations in a smooth domain
Jung, Chang-Yeol,Park, Eunhee,Temam, Roger De Gruyter 2017 Advances in nonlinear analysis Vol.6 No.3
<P>In this article, we consider a singularly perturbed nonlinear reaction-diffusion equation whose solutions display thin boundary layers near the boundary of the domain. We fully analyse the singular behaviours of the solutions at any given order with respect to the small parameter epsilon, with suitable asymptotic expansions consisting of the outer solutions and of the boundary layer correctors. The systematic treatment of the nonlinear reaction terms at any given order is novel along the singular perturbation analysis. We believe that the analysis can be suitably extended to other nonlinear problems.</P>
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