Asymptotic behavior of solutions to porous medium equations with boundary degeneracy
Asymptotic behavior of solutions to porous medium equations with boundary degeneracy
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DOI：
10.58997/ejde.2021.96
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发表时间：
2021-12
影响因子：
0.7
通讯作者：
XU Hao;Mingjun Zhou;Xinxin Jing
中科院分区：
文献类型：
--
作者：
XU Hao;Mingjun Zhou;Xinxin Jing
研究了一类具有边界退化的一维多孔介质方程解在有界和无界区间上的渐近性态。证明了退化度、非线性扩散指数和非线性源对解的渐近性态有影响。证明了在有界区间上，当退化不强时，该问题存在非平凡整体解和爆破解;当退化足够强时，任何非平凡解都必须爆破.对于无界区间上的问题，建立了Fujita型爆破定理。当简并性不强时，临界Fujita指数为有限;当简并性足够强时，临界Fujita指数为无限。进一步证明了临界情形是爆破情形，如果它是有限的。欲了解更多信息，请访问https://ejde.math.txstate.edu/Volumes/2021/96/abstr.html
This article concerns the asymptotic behavior of solutions to a class of one-dimensional porous medium equations with boundary degeneracy on bounded and unbounded intervals. It is proved that the degree of degeneracy, the exponents of the nonlinear diffusion, and the nonlinear source affect the asymptotic behavior of solutions. It is shown that on a bounded interval, the problem admits both nontrivial global and blowing-up solutions if the degeneracy is not strong; while any nontrivial solution must blow up if the degeneracy is strong enough. For the problem on an unbounded interval, the blowing-up theorems of Fujita type are established. The critical Fujita exponent is finite if the degeneracy is not strong, while infinite if the degeneracy is strong enough. Furthermore, the critical case is proved to be the blowing-up case if it is finite. For more information see https://ejde.math.txstate.edu/Volumes/2021/96/abstr.html