Asymptotic behavior of solutions to the Helmholtz equations with sign changing coefficients
Asymptotic behavior of solutions to the Helmholtz equations with sign changing coefficients
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具有变号系数的亥姆霍兹方程解的渐近行为
DOI：
10.1090/s0002-9947-2014-06305-8
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发表时间：
2012
影响因子：
1.3
通讯作者：
Hoai
中科院分区：
文献类型：
--
作者：
Hoai
本文致力于研究行为的唯一解u三角洲是一个元素的H-0(1)(ω),δ- > 0时,方程的div (s(δ)德尔u(δ))+ k (2) s(0)σu(δ)=ωs0 f,ω是一个光滑连接的有界开子集与d = 2或3 r d, f是一个元素的l2(ω),k是一个非负常数,一个是一个均匀椭圆matrixvalued函数,σ是一个真正的函数有界的上方和下方的积极的常数,s（）是一个复函数它的实部取1和1它的虚部是正的当趋于0时收敛于0。这源于Nicorovici， McPhedran和Milton的研究结果；另一个动机是互补媒体的概念。在引入反射互补介质，由反射产生的互补介质后，我们描述了f的特征，其中平行于u的δ在趋于0时保持有界。对于这样的一个f，我们也证明了u（）在H1(Q)上弱收敛，并给出了一个计算极限的公式。
This paper is devoted to the study of the behavior of the unique solution u delta is an element of H-0(1)(Omega), as delta -> 0, to the equation div(s(delta)A del u(delta)) + k(2)s(0)Sigma u(delta) = s0 f in Omega, where Omega is a smooth connected bounded open subset of R-d with d = 2 or 3, f is an element of L-2(Omega), k is a non-negative constant, A is a uniformly elliptic matrixvalued function, Sigma is a real function bounded above and below by positive constants, and s(delta) is a complex function whose real part takes the values 1 and 1 and whose imaginary part is positive and converges to 0 as delta goes to 0. This is motivated from a result of Nicorovici, McPhedran, and Milton; another motivation is the concept of complementary media. After introducing the reflecting complementary media, complementary media generated by reflections, we characterize f for which parallel to u delta parallel to(Omega) remains bounded as goes to 0. For such an f, we also show that u(delta) converges weakly in H1(Q) and provide a formula to compute the limit.
影响因子：
2.4
作者：
R. Kohn;Jianfeng Lu;B. Schweizer;M. Weinstein
通讯作者：
R. Kohn;Jianfeng Lu;B. Schweizer;M. Weinstein