April  1998, 4(2): 321-338. doi: 10.3934/dcds.1998.4.321

Scattering in domains with many small obstacles

1. 

S.I.S.S.A., Via Beirut 2-4, 34013, Trieste, Italy

Received  August 1997 Published  February 1998

We study the behaviour of the wave operators for the relaxed wave equations corresponding to a $\gamma$-convergent sequence of measures. The model case is that of a sequence of domains with many small obstacles.
Citation: Rodica Toader. Scattering in domains with many small obstacles. Discrete & Continuous Dynamical Systems, 1998, 4 (2) : 321-338. doi: 10.3934/dcds.1998.4.321
[1]

Kenji Nakanishi. Modified wave operators for the Hartree equation with data, image and convergence in the same space. Communications on Pure & Applied Analysis, 2002, 1 (2) : 237-252. doi: 10.3934/cpaa.2002.1.237

[2]

Yi-Hsuan Lin. Reconstruction of penetrable obstacles in the anisotropic acoustic scattering. Inverse Problems & Imaging, 2016, 10 (3) : 765-780. doi: 10.3934/ipi.2016020

[3]

Fenglong Qu, Jiaqing Yang. On recovery of an inhomogeneous cavity in inverse acoustic scattering. Inverse Problems & Imaging, 2018, 12 (2) : 281-291. doi: 10.3934/ipi.2018012

[4]

Lu Zhao, Heping Dong, Fuming Ma. Inverse obstacle scattering for acoustic waves in the time domain. Inverse Problems & Imaging, 2021, 15 (5) : 1269-1286. doi: 10.3934/ipi.2021037

[5]

Julián Fernández Bonder, Analía Silva, Juan F. Spedaletti. Gamma convergence and asymptotic behavior for eigenvalues of nonlocal problems. Discrete & Continuous Dynamical Systems, 2021, 41 (5) : 2125-2140. doi: 10.3934/dcds.2020355

[6]

Gianni Dal Maso. Ennio De Giorgi and $\mathbf\Gamma$-convergence. Discrete & Continuous Dynamical Systems, 2011, 31 (4) : 1017-1021. doi: 10.3934/dcds.2011.31.1017

[7]

Alexander Mielke. Deriving amplitude equations via evolutionary $\Gamma$-convergence. Discrete & Continuous Dynamical Systems, 2015, 35 (6) : 2679-2700. doi: 10.3934/dcds.2015.35.2679

[8]

Brian Sleeman. The inverse acoustic obstacle scattering problem and its interior dual. Inverse Problems & Imaging, 2009, 3 (2) : 211-229. doi: 10.3934/ipi.2009.3.211

[9]

Giorgio Menegatti, Luca Rondi. Stability for the acoustic scattering problem for sound-hard scatterers. Inverse Problems & Imaging, 2013, 7 (4) : 1307-1329. doi: 10.3934/ipi.2013.7.1307

[10]

Deyue Zhang, Yukun Guo. Some recent developments in the unique determinations in phaseless inverse acoustic scattering theory. Electronic Research Archive, 2021, 29 (2) : 2149-2165. doi: 10.3934/era.2020110

[11]

Mourad Sini, Nguyen Trung Thành. Inverse acoustic obstacle scattering problems using multifrequency measurements. Inverse Problems & Imaging, 2012, 6 (4) : 749-773. doi: 10.3934/ipi.2012.6.749

[12]

Jianliang Li, Jiaqing Yang, Bo Zhang. A linear sampling method for inverse acoustic scattering by a locally rough interface. Inverse Problems & Imaging, 2021, 15 (5) : 1247-1267. doi: 10.3934/ipi.2021036

[13]

Sylvia Serfaty. Gamma-convergence of gradient flows on Hilbert and metric spaces and applications. Discrete & Continuous Dynamical Systems, 2011, 31 (4) : 1427-1451. doi: 10.3934/dcds.2011.31.1427

[14]

Antonio De Rosa, Domenico Angelo La Manna. A non local approximation of the Gaussian perimeter: Gamma convergence and Isoperimetric properties. Communications on Pure & Applied Analysis, 2021, 20 (5) : 2101-2116. doi: 10.3934/cpaa.2021059

[15]

Lorenza D'Elia. $ \Gamma $-convergence of quadratic functionals with non uniformly elliptic conductivity matrices. Networks & Heterogeneous Media, 2021  doi: 10.3934/nhm.2021022

[16]

Charles L. Epstein, Leslie Greengard, Thomas Hagstrom. On the stability of time-domain integral equations for acoustic wave propagation. Discrete & Continuous Dynamical Systems, 2016, 36 (8) : 4367-4382. doi: 10.3934/dcds.2016.36.4367

[17]

Gang Bao, Mingming Zhang, Bin Hu, Peijun Li. An adaptive finite element DtN method for the three-dimensional acoustic scattering problem. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 61-79. doi: 10.3934/dcdsb.2020351

[18]

Xiaoxu Xu, Bo Zhang, Haiwen Zhang. Uniqueness in inverse acoustic and electromagnetic scattering with phaseless near-field data at a fixed frequency. Inverse Problems & Imaging, 2020, 14 (3) : 489-510. doi: 10.3934/ipi.2020023

[19]

Marc Bonnet. Inverse acoustic scattering using high-order small-inclusion expansion of misfit function. Inverse Problems & Imaging, 2018, 12 (4) : 921-953. doi: 10.3934/ipi.2018039

[20]

Jian Zhai, Zhihui Cai. $\Gamma$-convergence with Dirichlet boundary condition and Landau-Lifshitz functional for thin film. Discrete & Continuous Dynamical Systems - B, 2009, 11 (4) : 1071-1085. doi: 10.3934/dcdsb.2009.11.1071

2020 Impact Factor: 1.392

Metrics

  • PDF downloads (46)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]