Blow-up of solutions for weakly coupled systems of complex Ginzburg-Landau equations
Blow-up of solutions for weakly coupled systems of complex Ginzburg-Landau equations
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发表时间：
2017-07
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通讯作者：
K. Fujiwara;M. Ikeda;Yuta Wakasugi
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作者：
K. Fujiwara;M. Ikeda;Yuta Wakasugi
用一种简单的ODE方法，而不是所谓的测试函数法，给出了若干演化方程弱耦合系统的爆破现象，特别是复杂的金兹堡-朗道方程的爆破现象。证明的困难之处在于，与单一情况不同，来自拉普拉斯函数不能被弱耦合非线性吸收的事实的项。Mochizuki将类似的ODE方法应用于热系统，以获得较低的寿命估计。
Blow-up phenomena ofvweakly coupled systems of several evolution equations, especially complex Ginzburg-Landau equationsvis shown by a straightforward ODE approach not so-called test-function method, which gives the natural blow-up rate. The difficulty of the proof is that, unlike the single case, terms which come from the fact that 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.