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

Long-time averaging for some conservative PDEs having quadratic nonlinearities

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.
Citation: Steve Schochet. Long-time averaging for some conservative PDEs having quadratic nonlinearities. Discrete & Continuous Dynamical Systems - A, 2004, 11 (1) : 221-233. doi: 10.3934/dcds.2004.11.221
[1]

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

[2]

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

[3]

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

[4]

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

[5]

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

[6]

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

[7]

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

[8]

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

[9]

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

[10]

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

[11]

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

[12]

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

[13]

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

[14]

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

[15]

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

[16]

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

[17]

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

[18]

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

[19]

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

[20]

Frank Neubrander, Koray Özer, Teresa Sandmaier. Rational approximations of semigroups without scaling and squaring. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 5305-5317. doi: 10.3934/dcds.2013.33.5305

2018 Impact Factor: 1.143

Metrics

  • PDF downloads (11)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]