American Institute of Mathematical Sciences

Advanced
January  2004, 11(1): 221-233. doi: 10.3934/dcds.2004.11.221

Long-time averaging for some conservative PDEs having quadratic nonlinearities

Steve Schochet 1,

1. 

School of Mathematical Sciences, Tel-Aviv University, Ramat Aviv 69978, Israel

Received  January 2003 Revised  December 2003 Published  April 2004

The leading-order asymptotics through times of the order of the inverse square of the amplitude are determined for solutions to certain conservative PDEs having quadratic nonlinearities. This time scale is much longer than in standard averaging results.
Keywords: resonance, Averaging, asymptotics., scaling.
Mathematics Subject Classification: 35B40,35C2.
Citation: Steve Schochet. Long-time averaging for some conservative PDEs having quadratic nonlinearities. Discrete and Continuous Dynamical Systems, 2004, 11 (1) : 221-233. doi: 10.3934/dcds.2004.11.221
[1]

Christian Lax, Sebastian Walcher. Singular perturbations and scaling. Discrete and Continuous Dynamical Systems - B, 2020, 25 (1) : 1-29. doi: 10.3934/dcdsb.2019170
[2]

M. Baake, P. Gohlke, M. Kesseböhmer, T. Schindler. Scaling properties of the Thue–Morse measure. Discrete and Continuous Dynamical Systems, 2019, 39 (7) : 4157-4185. doi: 10.3934/dcds.2019168
[3]

Shinsuke Koyama, Ryota Kobayashi. Fluctuation scaling in neural spike trains. Mathematical Biosciences & Engineering, 2016, 13 (3) : 537-550. doi: 10.3934/mbe.2016006
[4]

Sohana Jahan. Discriminant analysis of regularized multidimensional scaling. Numerical Algebra, Control and Optimization, 2021, 11 (2) : 255-267. doi: 10.3934/naco.2020024
[5]

S. L. Ma'u, P. Ramankutty. An averaging method for the Helmholtz equation. Conference Publications, 2003, 2003 (Special) : 604-609. doi: 10.3934/proc.2003.2003.604
[6]

Natalia Skripnik. Averaging of fuzzy integral equations. Discrete and Continuous Dynamical Systems - B, 2017, 22 (5) : 1999-2010. doi: 10.3934/dcdsb.2017118
[7]

Jijiang Sun, Chun-Lei Tang. Resonance problems for Kirchhoff type equations. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 2139-2154. doi: 10.3934/dcds.2013.33.2139
[8]

Janusz Mierczyński. Averaging in random systems of nonnegative matrices. Conference Publications, 2015, 2015 (special) : 835-840. doi: 10.3934/proc.2015.0835
[9]

Jinxin Xue. Continuous averaging proof of the Nekhoroshev theorem. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 3827-3855. doi: 10.3934/dcds.2015.35.3827
[10]

Sergiu Aizicovici, Nikolaos S. Papageorgiou, Vasile Staicu. Nonlinear Dirichlet problems with double resonance. Communications on Pure and Applied Analysis, 2017, 16 (4) : 1147-1168. doi: 10.3934/cpaa.2017056
[11]

Andrej V. Plotnikov, Tatyana A. Komleva, Liliya I. Plotnikova. The averaging of fuzzy hyperbolic differential inclusions. Discrete and Continuous Dynamical Systems - B, 2017, 22 (5) : 1987-1998. doi: 10.3934/dcdsb.2017117
[12]

Peng Gao, Yong Li. Averaging principle for the Schrödinger equations†. Discrete and Continuous Dynamical Systems - B, 2017, 22 (6) : 2147-2168. doi: 10.3934/dcdsb.2017089
[13]

Leszek Gasiński, Nikolaos S. Papageorgiou. Dirichlet $(p,q)$-equations at resonance. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 2037-2060. doi: 10.3934/dcds.2014.34.2037
[14]

D. Bonheure, C. Fabry. A variational approach to resonance for asymmetric oscillators. Communications on Pure and Applied Analysis, 2007, 6 (1) : 163-181. doi: 10.3934/cpaa.2007.6.163
[15]

Philip Korman. Curves of equiharmonic solutions, and problems at resonance. Discrete and Continuous Dynamical Systems, 2014, 34 (7) : 2847-2860. doi: 10.3934/dcds.2014.34.2847
[16]

Robert McOwen, Peter Topalov. Asymptotics in shallow water waves. Discrete and Continuous Dynamical Systems, 2015, 35 (7) : 3103-3131. doi: 10.3934/dcds.2015.35.3103
[17]

Magnus Aspenberg, Fredrik Ekström, Tomas Persson, Jörg Schmeling. On the asymptotics of the scenery flow. Discrete and Continuous Dynamical Systems, 2015, 35 (7) : 2797-2815. doi: 10.3934/dcds.2015.35.2797
[18]

Nakao Hayashi, Pavel I. Naumkin, Isahi Sánchez-Suárez. Asymptotics for the modified witham equation. Communications on Pure and Applied Analysis, 2018, 17 (4) : 1407-1448. doi: 10.3934/cpaa.2018069
[19]

Fernando P. da Costa, João T. Pinto, Rafael Sasportes. On the convergence to critical scaling profiles in submonolayer deposition models. Kinetic and Related Models, 2018, 11 (6) : 1359-1376. doi: 10.3934/krm.2018053
[20]

Sohana Jahan, Hou-Duo Qi. Regularized multidimensional scaling with radial basis functions. Journal of Industrial and Management Optimization, 2016, 12 (2) : 543-563. doi: 10.3934/jimo.2016.12.543

2021 Impact Factor: 1.588

Tools

Metrics

  • PDF downloads (105)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy