共查询到20条相似文献,搜索用时 15 毫秒
1.
Using a capacity approach, we prove in this article that it is always possible to define a realization of the Laplacian on L
2() with generalized Robin boundary conditions where is an arbitrary open subset of R
n
and is a Borel measure on the boundary of . This operator generates a sub-Markovian C
0-semigroup on L
2(). If d=d where is a strictly positive bounded Borel measurable function defined on the boundary and the (n–1)-dimensional Hausdorff measure on , we show that the semigroup generated by the Laplacian with Robin boundary conditions has always Gaussian estimates with modified exponents. We also obtain that the spectrum of the Laplacian with Robin boundary conditions in L
p
() is independent of p[1,). Our approach constitutes an alternative way to Daners who considers the (n–1)-dimensional Hausdorff measure on the boundary. In particular, it allows us to construct a conterexample disproving Daners' closability conjecture. 相似文献
2.
Kwangil Kim & Yonghai Li 《计算数学(英文版)》2015,33(3):227-247
We study numerical methods for time-dependent Hamilton-Jacobi equations with weak Dirichlet boundary conditions. We first propose a new class of abstract monotone approximation schemes and get a convergence rate of 1/2 . Then, according to the abstract convergence results, by newly constructing monotone finite volume approximations on interior and boundary points, we obtain convergent finite volume schemes for time-dependent Hamilton-Jacobi equations with weak Dirichlet boundary conditions. Finally give some numerical results. 相似文献
3.
The existence of a full asymptotic expansion for the heat content asymptotics of an operator of Laplace type with classical
Zaremba boundary conditions on a smooth manifold is established. The first three coefficients in this asymptotic expansion
are determined in terms of geometric invariants; partial information is obtained about the fourth coefficient.
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In this paper we introduce the abstract concept of “linear boundary conditions” in the study of deformable bodies. We establish two existence and uniqueness results concerning respectively quasistatic and dynamic problems involving such type of boundary conditions. We also apply these existence results in the study of viscoplastic problems involving classical boundary conditions. 相似文献
6.
Paweł Konieczny 《Acta Appl Math》2009,106(1):61-77
The paper examines the issue of existence of solutions to the steady Navier-Stokes equations in an exterior domain in ℝ2. The system is studied with nonhomogeneous slip boundary conditions. The main results proves the existence of weak solutions
for arbitrary data.
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7.
Let M be a compact manifold with smooth boundary. We establish the existence of an asymptotic expansion for the heat content asymptotics of M with inhomogeneous Neumann and Dirichlet boundary conditions. We prove all the coefficients are locally determined and determine the first several terms in the asymptotic expansion. 相似文献
8.
Lower Bound Estimate of Blow Up Time for the Porous Medium Equations under Dirichlet and Neumann Boundary Conditions
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Yingzhen Xue 《偏微分方程(英文版)》2021,34(1):94-102
In this paper, we establish the lower bounds estimate of the blow up time
for solutions to the nonlocal cross-coupled porous medium equations with nonlocal
source terms under Dirichlet and Neumann boundary conditions. The results are obtained by using some differential inequality technique. 相似文献
9.
Wang Yi Fan Yizheng Tan Yingying 《高校应用数学学报(英文版)》2007,22(4):478-484
In this paper,an equivalent condition of a graph G with t(2≤t≤n)distinct Laplacian eigenvalues is established.By applying this condition to t=3,if G is regular(neces- sarily be strongly regular),an equivalent condition of G being Laplacian integral is given.Also for the case of t=3,if G is non-regular,it is found that G has diameter 2 and girth at most 5 if G is not a tree.Graph G is characterized in the case of its being triangle-free,bipartite and pentagon-free.In both cases,G is Laplacian integral. 相似文献
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Fa-en WU~ 《中国科学A辑(英文版)》2007,50(8):1078-1086
Let D be a bounded domain in an n-dimensional Euclidean space Rn. Assume that 0 < λ1 ≤λ2 ≤ … ≤ λκ ≤ … are the eigenvalues of the Dirichlet Laplacian operator with any order l{(-△)lu=λu, in D u=(δ)u/(δ)(→n)=…(δ)l-1u/(δ)(→n)l-1=0,on (δ)D.Then we obtain an upper bound of the (k 1)-th eigenvalue λκ 1 in terms of the first k eigenvalues.k∑i=1(λκ 1-λi) ≤ 1/n[4l(n 2l-2)]1/2{k∑i=1(λκ 1-λi)1/2λil-1/l k∑i=1(λκ 1-λi)1/2λ1/li}1/2.This ineguality is independent of the domain D. Furthermore, for any l ≥ 3 the above inequality is better than all the known results. Our rusults are the natural generalization of inequalities corresponding to the case l = 2 considered by Qing-Ming Cheng and Hong-Cang Yang. When l = 1, our inequalities imply a weaker form of Yang inequalities. We aslo reprove an implication claimed by Cheng and Yang. 相似文献
13.
常型Sturm-Liouville问题的左定边值条件 总被引:2,自引:0,他引:2
本文刻画了常型Sturm-Liouville问题的左定边值条件.通过Sturm-Liouville微分算式的系数、区间端点以及边值条件给出了其左定性的充要条件.应用自伴边值条件分类,确切地给出了所有可能的左定边值条件. 相似文献
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全无赘数irt是图的一个重要参数.本文对irt=0的正则图的结构进行了探讨,提供了构造irt=0的正则图的一个方法. 相似文献
16.
Giles Auchmuty 《Numerical Functional Analysis & Optimization》2018,39(10):999-1010
This paper describes the rate of convergence of solutions of Robin boundary value problems of an elliptic equation to the solution of a Dirichlet problem as a boundary parameter decreases to zero. The results are found using representations for solutions of the equations in terms of Steklov eigenfunctions. Particular interest is in the case where the Dirichlet data is only in L2(?Ω,dσ). Various approximation bounds are obtained and the rate of convergence of the Robin approximations in the H1 and L2 norms are shown to have convergence rates that depend on the regularity of the Dirichlet data. 相似文献
17.
M. M. Cavalcanti V. N. Domingos Cavalcanti J. A. Soriano L. A. Medeiros 《Southeast Asian Bulletin of Mathematics》2000,24(2):183-199
In this paper, we study a hyperbolic model based on the equation
with nonlinear boundary conditions given by
.We prove the existence and the uniqueness of global solutions. Also, we obtain the uniform decay of the energy without control of its derivative sign.AMS Subject Classification (2000), 35L05, 35L70, 35B40 相似文献
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We investigate the basic boundary value problems of the connected theory of elastothermodiffusion for three-dimensional domains bounded by several closed surfaces when the same boundary conditions are fulfilled on every separate boundary surface, but these conditions differ on different groups of surfaces. Using the results of papers [1–8], we prove theorems on the existence and uniqueness of the classical solutions of these problems. 相似文献