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Yan, Guozheng; Yao, Mao

On the nonexistence of transmission eigenvalues for regions with cavities. (English) Zbl 1231.35136

Commun. Partial Differ. Equations 36, No. 7-9, 1510-1519 (2011).
Authors’ abstract: We consider the interior transmission problem when the inhomogeneous medium has a cavity region. In this case we establish the Fredholm property for this problem and show that there does not exist a transmission eigenvalue under a new condition.
Reviewer: Alla Boikova (Penza)

Cited in 1 Document

MSC:

35P25 Scattering theory for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35R30 Inverse problems for PDEs

Keywords:

Helmholtz equation; scattering problem; transmission eigenvalues
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References:

[1] DOI: 10.1216/JIE-2009-21-2-179 · Zbl 1237.65118 · doi:10.1216/JIE-2009-21-2-179
[2] DOI: 10.1088/0266-5611/17/6/316 · Zbl 0987.78019 · doi:10.1088/0266-5611/17/6/316
[3] Cakoni F., Qualitative Methods in Inverse Scattering Theory (2006) · Zbl 1099.78008
[4] DOI: 10.1137/090754637 · Zbl 1209.35135 · doi:10.1137/090754637
[5] DOI: 10.1137/090769338 · Zbl 1210.35282 · doi:10.1137/090769338
[6] DOI: 10.3934/ipi.2007.1.443 · Zbl 1149.35078 · doi:10.3934/ipi.2007.1.443
[7] DOI: 10.1080/00036810802713966 · Zbl 1168.35448 · doi:10.1080/00036810802713966
[8] DOI: 10.1137/0520096 · Zbl 0681.76084 · doi:10.1137/0520096
[9] Colton D., Inverse Acoustic and Electromagnetic Scattering Theory (1998) · Zbl 0893.35138 · doi:10.1007/978-3-662-03537-5
[10] DOI: 10.1093/qjmam/41.1.97 · Zbl 0637.73026 · doi:10.1093/qjmam/41.1.97
[11] DOI: 10.3934/ipi.2007.1.13 · Zbl 1130.35132 · doi:10.3934/ipi.2007.1.13
[12] DOI: 10.1002/mma.465 · Zbl 1062.35168 · doi:10.1002/mma.465
[13] DOI: 10.3934/ipi.2007.1.159 · Zbl 1129.35080 · doi:10.3934/ipi.2007.1.159
[14] DOI: 10.3934/ipi.2009.3.155 · Zbl 1186.35122 · doi:10.3934/ipi.2009.3.155
[15] DOI: 10.1093/imamat/61.3.267 · Zbl 0922.73013 · doi:10.1093/imamat/61.3.267
[16] DOI: 10.1137/070697525 · Zbl 1159.81411 · doi:10.1137/070697525
[17] DOI: 10.1137/0522109 · Zbl 0733.76065 · doi:10.1137/0522109
[18] DOI: 10.1088/0266-5611/18/3/301 · Zbl 0998.35065 · doi:10.1088/0266-5611/18/3/301
[19] DOI: 10.1088/0266-5611/16/6/311 · Zbl 0978.35099 · doi:10.1088/0266-5611/16/6/311
[20] DOI: 10.1121/1.429441 · doi:10.1121/1.429441
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