共查询到20条相似文献,搜索用时 8 毫秒
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Gleiciane S. Aragão Simone M. Bruschi 《Mathematical Methods in the Applied Sciences》2016,39(12):3450-3460
In this paper, we analyze the behavior of a family of solutions of a nonlinear elliptic equation with nonlinear boundary conditions, when the boundary of the domain presents a highly oscillatory behavior, which is uniformly Lipschitz and nonlinear terms, are concentrated in a region, which neighbors the boundary of domain. We prove that this family of solutions converges to the solutions of a limit problem in H1an elliptic equation with nonlinear boundary conditions which captures the oscillatory behavior of the boundary and whose nonlinear terms are transformed into a flux condition on the boundary. Indeed, we show the upper semicontinuity of this family of solutions.Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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This paper is concerned with exact boundary behavior of large solutions to semilinear elliptic equations △u=b(x)f(u)(C0+|▽u|q),x∈Ω,where Ω is a bounded domain with a smooth boundary in RN,C0≥0,q E [0,2),b∈Clocα(Ω) is positive in but may be vanishing or appropriately singular on the boundary,f∈C[0,∞),f(0)=0,and f is strictly increasing on [0,∞)(or f∈C(R),f(s)> 0,■s∈R,f is strictly increasing on R).We show unified boundary behavior of such solutions to the problem under a new structure condition on f. 相似文献
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闻国椿 《数学物理学报(B辑英文版)》2007,27(3):663-672
The present article deals with some boundary value problems for nonlinear elliptic equations with degenerate rank 0 including the oblique derivative problem.Firstly the formulation and estimates of solutions of the oblique derivative problem are given, and then by the above estimates and the method of parameter extension,the existence of solutions of the above problem is proved.In this article,the complex analytic method is used,namely the corresponding problem for degenerate elliptic complex equations of first order is firstly discussed,afterwards the above problem for the degenerate elliptic equations of second order is solved. 相似文献
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MoJiaqi LinWantao 《高校应用数学学报(英文版)》2005,20(2):159-164
The singularly perturbed boundary value problem for the nonlinear boundary conditions is considered. Under suitable conditions,the asymptotic behavior of solution for the original problems is studied by using theory of differential inequalities. 相似文献
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T. Shibata 《Transactions of the American Mathematical Society》2004,356(5):2123-2135
We consider the nonlinear singularly perturbed problem
where () is an appropriately smooth bounded domain and 0$"> is a small parameter. It is known that under some conditions on , the solution corresponding to develops boundary layers when . We determine the steepest point of the boundary layers on the boundary by establishing an asymptotic formula for the slope of the boundary layers with exact second term.
0 \quad \mbox{in} \enskip \Omega, u = 0 \quad \mbox{on} \enskip \partial\Omega, \end{displaymath}">
where () is an appropriately smooth bounded domain and 0$"> is a small parameter. It is known that under some conditions on , the solution corresponding to develops boundary layers when . We determine the steepest point of the boundary layers on the boundary by establishing an asymptotic formula for the slope of the boundary layers with exact second term.
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L. E. Bobisud 《Applicable analysis》2013,92(1-4):43-57
Existence of solutions to the two-point boundary value problem (p(t)y')' = q(t)f(t, y,p(t)y'), y(l) = 0, limt→0+ p(t)y'(t) = 0 is established under a variety of conditions. Here p(0) = 0 is allowed, and q is not assumed to be continuous at 0, so the problem may be doubly singular. In addition, the Dirichlet problem for this differential equation is investigated 相似文献
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I. V. Denisov 《Computational Mathematics and Mathematical Physics》2008,48(1):59-75
The Dirichlet problem in a rectangle is considered for the elliptic equation ?2Δu = F(u, x, y, ?), where F(u, x, y, ?) is a nonlinear function of u. The method of corner boundary functions is applied to the problem. Assuming that the leading term of the corner part of the asymptotics exists, an asymptotic expansion of the solution is constructed and the remainder is estimated. 相似文献
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Ángela Jiménez-Casas 《Journal of Mathematical Analysis and Applications》2011,379(2):567-588
We analyze the asymptotic behavior of the attractors of a parabolic problem when some reaction and potential terms are concentrated in a neighborhood of a portion Γ of the boundary and this neighborhood shrinks to Γ as a parameter ε goes to zero. We prove that the family of attractors is upper continuous at the ε=0. 相似文献
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研究了三阶非线性边值条件的非线性方程奇摄动问题,先用合成展开法对形式近似解进行构造,再利用相关微分不等式理论给出所得解的存在性及一致有效性的证明. 相似文献