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Stability for the acoustic scattering problem for sound-hard scatterers
1. | Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, via Valerio 12/1, 34127 Trieste, Italy |
2. | Dipartimento di Matematica e Informatica, Università degli Studi di Trieste, via Valerio, 12/1, 34127 Trieste |
  We obtain uniform decay estimates for scattered fields and we investigate how a sound-hard screen may be approximated by thin sound-hard obstacles.
References:
[1] |
R. A. Adams, Sobolev Spaces,, Academic Press, (1975).
|
[2] |
D. Bucur and N. Varchon, Stability of the Neumann problem for variations of boundary,, C. R. Acad. Sci. Paris Sér. I Math., 331 (2000), 371.
doi: 10.1016/S0764-4442(00)01668-2. |
[3] |
D. Bucur and N. Varchon, Boundary variation for a Neumann problem,, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 29 (2000), 807.
|
[4] |
A. Chambolle and F. Doveri, Continuity of Neumann linear elliptic problems on varying two-dimensional bounded open sets,, Comm. Partial Differential Equations, 22 (1997), 811.
doi: 10.1080/03605309708821285. |
[5] |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory,, Springer-Verlag, (1998).
|
[6] |
G. Dal Maso, An Introduction to $\Gamma$-Convergence,, Birkhäuser, (1993).
doi: 10.1007/978-1-4612-0327-8. |
[7] |
G. Dal Maso and R. Toader, A model for the quasi-static growth of brittle fractures: existence and approximation results,, Arch. Ration. Mech. Anal., 162 (2002), 101.
doi: 10.1007/s002050100187. |
[8] |
A. Giacomini, A stability result for Neumann problems in dimension $N\geq 3$,, J. Convex Anal., 11 (2004), 41.
|
[9] |
R. Kress, On the low wave number asymptotics for the two-dimensional exterior Dirichlet problem for the reduced wave equation,, Math. Meth. Appl. Sci., 9 (1987), 335.
doi: 10.1002/mma.1670090126. |
[10] |
J. Li, H. Liu, L. Rondi and G. Uhlmann, Regularized transformation-optics cloaking for the Helmholtz equation: from partial cloak to full cloak,, preprint, (2013). Google Scholar |
[11] |
F. Murat, The Neumann sieve,, in Nonlinear Variational Problems, (1985), 24.
|
[12] |
L. Rondi, Unique determination of non-smooth sound-soft scatterers by finite\-ly many far-field measurements,, Indiana Univ. Math. J., 52 (2003), 1631.
doi: 10.1512/iumj.2003.52.2394. |
[13] |
L. Rondi, Unique continuation from Cauchy data in unknown non-smooth domains,, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 5 (2006), 189.
|
[14] |
C. H. Wilcox, Scattering Theory for the d'Alembert Equation in Exterior Domains,, Springer-Verlag, (1975).
|
show all references
References:
[1] |
R. A. Adams, Sobolev Spaces,, Academic Press, (1975).
|
[2] |
D. Bucur and N. Varchon, Stability of the Neumann problem for variations of boundary,, C. R. Acad. Sci. Paris Sér. I Math., 331 (2000), 371.
doi: 10.1016/S0764-4442(00)01668-2. |
[3] |
D. Bucur and N. Varchon, Boundary variation for a Neumann problem,, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 29 (2000), 807.
|
[4] |
A. Chambolle and F. Doveri, Continuity of Neumann linear elliptic problems on varying two-dimensional bounded open sets,, Comm. Partial Differential Equations, 22 (1997), 811.
doi: 10.1080/03605309708821285. |
[5] |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory,, Springer-Verlag, (1998).
|
[6] |
G. Dal Maso, An Introduction to $\Gamma$-Convergence,, Birkhäuser, (1993).
doi: 10.1007/978-1-4612-0327-8. |
[7] |
G. Dal Maso and R. Toader, A model for the quasi-static growth of brittle fractures: existence and approximation results,, Arch. Ration. Mech. Anal., 162 (2002), 101.
doi: 10.1007/s002050100187. |
[8] |
A. Giacomini, A stability result for Neumann problems in dimension $N\geq 3$,, J. Convex Anal., 11 (2004), 41.
|
[9] |
R. Kress, On the low wave number asymptotics for the two-dimensional exterior Dirichlet problem for the reduced wave equation,, Math. Meth. Appl. Sci., 9 (1987), 335.
doi: 10.1002/mma.1670090126. |
[10] |
J. Li, H. Liu, L. Rondi and G. Uhlmann, Regularized transformation-optics cloaking for the Helmholtz equation: from partial cloak to full cloak,, preprint, (2013). Google Scholar |
[11] |
F. Murat, The Neumann sieve,, in Nonlinear Variational Problems, (1985), 24.
|
[12] |
L. Rondi, Unique determination of non-smooth sound-soft scatterers by finite\-ly many far-field measurements,, Indiana Univ. Math. J., 52 (2003), 1631.
doi: 10.1512/iumj.2003.52.2394. |
[13] |
L. Rondi, Unique continuation from Cauchy data in unknown non-smooth domains,, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 5 (2006), 189.
|
[14] |
C. H. Wilcox, Scattering Theory for the d'Alembert Equation in Exterior Domains,, Springer-Verlag, (1975).
|
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