Kazumasa Fujiwara, Masahiro Ikeda, Yuta Wakasugi
Abstract:
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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