Electron. J. Differential Equations, Vol. 2017 (2017), No. 196, pp. 1-16.

Blow-up of solutions for weakly coupled systems of complex Ginzburg-Landau equations

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 [38] 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 [32] 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
Waseda University
3-4-1, Okubo, Shinjuku-ku
Tokyo, 169-8555, Japan
email: k-fujiwara@asagi.waseda.jp
Masahiro Ikeda
Department of Mathematics
Faculty of Science and Technology
Keio University, 3-14-1 Hiyoshi, Kohoku-ku
Yokohama, 223-8522, Japan
email: masahiro.ikeda@keio.jp, masahiro.ikeda@riken.jp
Yuta Wakasugi
Department of Engineering for Production and Environment
Graduate School of Science and Engineering
Ehime University
3 Bunkyo-cho, Matsuyama, Ehime, 790-8577, Japan
email: wakasugi.yuta.vi@ehime-u.ac.jp

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