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arXiv · 1703.09094

Threshold results for the existence of global and blow-up solutions to Kirchhoff equations with arbitrary initial energy

Yuzhu Han·Qingwei Li
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Abstract

In this paper we will apply the modified potential well method and variational method to the study of the long time behaviors of solutions to a class of parabolic equation of Kirchhoff type. Global existence and blow up in finite time of solutions will be obtained for arbitrary initial energy. To be a little more precise, we will give a threshold result for the solutions to exist globally or to blow up in finite time when the initial energy is subcritical and critical, respectively. The decay rate of the $L^2(Ω)$ norm is also obtained for global solutions in these cases. Moreover, some sufficient conditions for the existence of global and blow-up solutions are also derived when the initial energy is supercritical.

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Yuzhu Han, Qingwei Li. 2017-03-27. Threshold results for the existence of global and blow-up solutions to Kirchhoff equations with arbitrary initial energy. https://arxiv.org/abs/1703.09094

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