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arXiv · 1703.09882

Classification of certain qualitative properties of solutions for the quasilinear parabolic equations

Yan Li·Zhengce Zhang·Liping Zhu
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Abstract

In this paper, we mainly consider the initial boundary problem for a quasilinear parabolic equation \[ u_t-\mathrm{div}\left(|\nabla u|^{p-2}\nabla u\right)=-|u|^{\beta-1}u+\alpha|u|^{q-2}u, \] where $p>1,\beta>0$, $q\geq1$ and $\alpha>0$. By using Gagliardo-Nirenberg type inequality, energy method and comparison principle, the phenomena of blowup and extinction are classified completely in the different ranges of reaction exponents.

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Yan Li, Zhengce Zhang, Liping Zhu. 2017-03-29. Classification of certain qualitative properties of solutions for the quasilinear parabolic equations. https://arxiv.org/abs/1703.09882

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