http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
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>
Koh, Youngwoo,Seo, Ihyeok Discrete and Continuous Dynamical Systems 2017 Discrete and continuous dynamical systems Vol.37 No.9
<P>We obtain weighted L-2 Strichartz estimates for Schrodinger equations i partial derivative(t)u + (-Delta)(u)(a/2) = F(x, t), u(x, 0) = f(x), of general orders a > 1 with radial data f, F with respect to the spatial variable x, whenever the weight is in a Morrey-Campanato type class. This is done by making use of a useful property of maximal functions of the weights together with frequency-localized estimates which follow from using bilinear interpolation and some estimates of Bessel functions. As consequences, we give an affirmative answer to a question posed in [1] concerning weighted homogeneous Strichartz estimates, and improve previously known Morawetz estimates. We also apply the weighted L-2 estimates to the well-posedness theory for the Schrodinger equations with time-dependent potentials in the class.</P>
Jin, Bum Ja,Kang, Kyungkeun Discrete and Continuous Dynamical Systems 2017 Discrete and continuous dynamical systems Vol.37 No.9
<P>We prove a Caccioppoli type inequality for the solution of a parabolic system related to the nonlinear Stokes problem. Using the method of Caccioppoli type inequality, we also establish the existence of weak solutions satisfying a local energy inequality without pressure for the non-Newtonian Navier-Stokes equations.</P>