Kazumasa Fujiwara, Masahiro Ikeda, Yuta Wakasugi
Blow-up phenomena of weakly coupled systems of several evolution equations, especially complex Ginzburg-Landau equations is shown by a straightforward ODE approach, not by the so-called test-function method used in  which gives the natural blow-up rate. The difficulty of the proof is that, unlike the single case, terms which come from the Laplacian cannot be absorbed into the weakly coupled nonlinearities. A similar ODE approach is applied to heat systems by Mochizuki  to obtain the lower estimate of lifespan.
Submitted July 22, 2017. Published August 8, 2017.
Math Subject Classifications: 35B44, 35Q55.
Key Words: Weakly coupled; complex Ginzburg-Landau equation; blow-up.
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| Kazumasa Fujiwara |
Department of Pure and Applied Physics
3-4-1, Okubo, Shinjuku-ku
Tokyo, 169-8555, Japan
| Masahiro Ikeda |
Department of Mathematics
Faculty of Science and Technology
Keio University, 3-14-1 Hiyoshi, Kohoku-ku
Yokohama, 223-8522, Japan
email: firstname.lastname@example.org, email@example.com
| Yuta Wakasugi |
Department of Engineering for Production and Environment
Graduate School of Science and Engineering
3 Bunkyo-cho, Matsuyama, Ehime, 790-8577, Japan
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