Global behavior of solutions to chevron pattern equations
Abstract
Considering a system of equations modeling the chevron pattern dynamics, we show that the corresponding initial boundary value problem has a unique weak solution that continuously depends on initial data, and the semigroup generated by this problem in the phase space $X^0:= L^2(\Omega)\times L^2(\Omega)$ has a global attractor. We also provide some insight to the behavior of the system, by reducing it under special assumptions to systems of ODEs, that can in turn be studied as dynamical systems.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 June 2020
 DOI:
 10.1063/5.0012525
 arXiv:
 arXiv:1910.04676
 Bibcode:
 2020JMP....61f1511K
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics;
 Nonlinear Sciences  Pattern Formation and Solitons;
 35K55;
 35B41;
 49N60;
 76A15
 EPrint:
 doi:10.1063/5.0012525