On considère des perturbations régulières et singulières des problèmes aux limites de Dirichlet et de Neumann pour l'équation de Helmholtz dans les cylindres n-dimensionnels. Sont étudies l'existence des valeurs propres et de leur comportement asymptotique.
We consider regular and singular perturbations of the Dirichlet and Neumann boundary value problems for the Helmholtz equation in n-dimensional cylinders. The existence of eigenvalues and their asymptotics are studied.
Accepté le :
Publié le :
Mot clés : Acoustique, Guide d'ondes, Perturbation, Valeur propre
Rustem R. Gadyl'shin 1, 2
@article{CRMECA_2004__332_8_647_0, author = {Rustem R. Gadyl'shin}, title = {On regular and singular perturbations of acoustic and quantum waveguides}, journal = {Comptes Rendus. M\'ecanique}, pages = {647--652}, publisher = {Elsevier}, volume = {332}, number = {8}, year = {2004}, doi = {10.1016/j.crme.2004.03.010}, language = {en}, }
Rustem R. Gadyl'shin. On regular and singular perturbations of acoustic and quantum waveguides. Comptes Rendus. Mécanique, Volume 332 (2004) no. 8, pp. 647-652. doi : 10.1016/j.crme.2004.03.010. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.03.010/
[1] On local perturbations of Shrödinger operator in axis, Teor. Mat. Fiz., Volume 132 (2002) no. 1, pp. 97-104 (English translation Theor. Math. Phys., 132, 1, 2002, pp. 976-982)
[2] Curvature-induced bound states in quantum waveguides in two and three dimensions, Rev. Math. Phys., Volume 7 (1995), pp. 73-102
[3] Weakly coupled bound states in quantum waveguides, Proc. Amer. Math. Soc., Volume 127 (1997), pp. 1487-1495
[4] Bound states in a locally deformed waveguide: the critical case, Lett. Math. Phys., Volume 39 (1997), pp. 59-68
[5] Bound states in weakly deformed strips and layers, Ann. Inst. H. Poincaré, Volume 2 (2001) no. 3, pp. 553-572
[6] Asymptotic estimates for bound states in quantum waveguides coupled laterally through a narrow window, Ann. Inst. H. Poincaré: Phys. Théor., Volume 65 (1996), pp. 109-123
[7] Asymptotics of bounded states for laterally coupled three-dimensional waveguides, Rep. Math. Phys., Volume 48 (2001), pp. 277-288
[8] Three laterally coupled quantum waveguiedes: breaking of symmetry and resonance asymptotics, J. Phys. A, Volume 36 (2003), pp. 1655-1670
[9] Matching of Asymptotic Expansions of Solutions of Boundary Value Problems, American Mathematical Society, Providence, RI, 1992
[10] Surface potentials and the method of matching asymptotic expansions in the problem of the Helmholtz resonator, Algebra Anal., Volume 4 (1992) no. 2, pp. 88-115 (English translation St. Petersburg Math. J., 4, 1, 1993, pp. 273-296)
[11] On acoustic Helmholtz resonator and on its electromagnetic analog, J. Math. Phys., Volume 35 (1994) no. 7, pp. 3464-3481
[12] Existence and asymptotics of poles with small imaginary part for the Helmholtz resonator, Uspekhi Mat. Nauk, Volume 52 (1997) no. 1, pp. 3-76 (English translation Russian Math. Surveys, 52, 1, 1997, pp. 1-72)
[13] Non-Homogeneous Media and Vibration Theory, Springer-Verlag, New York, 1980
[14] On analogs of Helmholtz resonator in averaging theory, Mat. Sb., Volume 193 (2002) no. 11, pp. 43-70 (English translation Sb. Math., 193, 11, 2002, pp. 1611-1638)
Cité par Sources :
Commentaires - Politique