2005/03/15 by Nikos I. Karachalios, Karachalios, Nikos I., Hector E. Nistazakis +3
Computer Science · Mathematics · Medicine · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #math.CA #math.DS
paper · pdf · doi:10.48550/arxiv.math/0503297
arxiv created 2005/03/15 · openalex publication_date 2005/03/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the asymptotic behavior of complex discrete evolution equations of Ginzburg- Landau type. Depending on the nonlinearity and the data of the problem, we find different dynamical behavior ranging from global existence of solutions and global attractors, to blow up in finite time. We provide estimates for the blow up time, depending not only on the initial data but also on the size of the lattice. Some of the theoretical results, are tested by numerical simulations.