Geodesic
Breather collapse for a dispersive effective equation: asymptotics on the well-posedness boundary
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 7, pp. 1276-1284 
S. I. Serdyukova. Breather collapse for a dispersive effective equation: asymptotics on the well-posedness boundary. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 7, pp. 1276-1284. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_7_a9/
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     title = {Breather collapse for a dispersive effective equation: asymptotics on the well-posedness boundary},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1276--1284},
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     number = {7},
     language = {ru},
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Voir la notice de l'article provenant de la source Math-Net.Ru

For the solution of the Cauchy problem for the equation $$ u_{tt}=u_{xx}+i2u_{ttx}+u_{ttxx} $$ with discontinuous initial data, asymptotic formulas as $t\to\infty$ are derived, which agree well with numerical results. The stability of the numerical methods used is analyzed. Other results are presented concerning nonstandard linear equations produced by homogenizing the equations describing wave processes in periodic stratified media.

[1] Bakhvalov N. S., Eglit M. E., “Effektivnye uravneniya s dispersiei dlya rasprostraneniya voln v periodicheskikh sredakh”, Dokl. AN, 370:1 (2000), 7–11 | MR

[2] Bakhvalov N. S., Eglit M. E., “Issledovanie effektivnykh uravnenii s dispersiei, opisyvayuschikh rasprostranenie voln v stratifitsirovannykh sloistykh sredakh i tonkikh plastinakh”, Dokl. AN, 383:6 (2002), 742–746 | MR | Zbl

[3] Serdyukova S. I., “Ekzoticheskaya asimptotika dlya lineinogo giperbolicheskogo uravneniya”, Dokl. AN, 389:3 (2003), 1–5 | MR

[4] Serdyukova S. I., “Zhestkii perekhod ot statsionarnogo sostoyaniya k kolebaniyam dlya lineinogo differentsialnogo uravneniya”, Dokl. AN. Matematika, 415:3 (2007), 310–314 | MR | Zbl

[5] Serdyukova S. I., “Deformatsiya resheniya tipa brizer pri dobavlenii mladshego chlena s kompleksnym koeffitsientom”, Dokl. AN. Matematika, 427:1 (2009), 17–23 | MR | Zbl

[6] Vladimirov V. S., Uravneniya matematicheskoi fiziki, Nauka, M., 1988 | MR

[7] Petrovskii I. G., “O probleme Koshi dlya sistem lineinykh uravnenii s chastnymi proizvodnymi v oblasti neanaliticheskikh funktsii”, Byull. MGU, sekts. A, 1938, no. 1 | MR

[8] Fedoryuk M. V., Asimptotika: Integraly i ryady, Nauka, M., 1987 | MR

[9] Winfried Neun (ed.), REDUCE User's guide for unix systems. Version 3.8, ZiB D-14195, Berlin-Dahlem, Sept. 2004