A rigorous justification of the Matthews–Cox approximation for the Nikolaevskiy equation

Autor:	Dominik Zimmermann
Rok vydání:	2017
Předmět:	Independent equation Applied Mathematics 010102 general mathematics Mathematical analysis Pattern formation Rigorous proof 01 natural sciences 010305 fluids & plasmas Amplitude 0103 physical sciences Modulation (music) Applied mathematics 0101 mathematics Scaling Analysis Ansatz Mathematics
Zdroj:	Journal of Differential Equations. 262:5409-5424
ISSN:	0022-0396
DOI:	10.1016/j.jde.2017.02.005
Popis:	The Nikolaevskiy equation is an example of a pattern forming system with marginally stable long modes. It has the unusual property that the typical Ginzburg–Landau scaling ansatz for the description of propagating patterns does not yield asymptotically consistent amplitude equations. Instead, another scaling proposed by Matthews and Cox can be used to formally derive a consistent system of modulation equations. We give a rigorous proof that this system makes correct predictions about the dynamics of the Nikolaevskiy equation.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::4689c3d2cf237a7010231bbe38e43986 https://doi.org/10.1016/j.jde.2017.02.005 Zobrazit plný text záznamu Full Text from ScienceDirect