Asymptotic behavior of solutions to coupled porous medium systems with boundary degeneracy
Asymptotic behavior of solutions to coupled porous medium systems with boundary degeneracy
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DOI：
10.58997/ejde.2022.73
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发表时间：
2022-10
影响因子：
0.7
通讯作者：
Xutong Zhao;Mingjun Zhou;Qian Zhou
中科院分区：
文献类型：
--
作者：
Xutong Zhao;Mingjun Zhou;Qian Zhou
本文研究了具有边界退化的一维多孔介质系统解在有界和无界区间内的渐近性态。结果表明，边界退化程度和非线性扩散指数决定解的渐近行为。对于有界区间上的问题，如果退化性不强，则该问题存在非平凡整体解和爆破解，而如果退化性足够强，则该问题的任何非平凡解都必须在有限时间内爆破.对于无界区间上的问题，建立了Fujita型爆破定理，并由边界退化度和非线性扩散指数给出了临界Fujita指数.
This article concerns the asymptotic behavior of solutions of one-dimensional porous medium systems with boundary degeneracy in bounded and unbounded intervals. It is shown that the degree of the boundary degeneracy and the exponent of the nonlinear diffusion determine asymptotic behaviors of solutions. For the problem in a bounded interval, if the degeneracy is not strong, the problem admits both nontrivial global and blowing-up solutions, while if the degeneracy is strong enough, any nontrivial solution to the problem must blow up in a finite time. For the problem in an unbounded interval, the Fujita type blowing-up theorems are established and the critical Fujita exponent is formulated by the degree of the boundary degeneracy and the exponent of nonlinear diffusion.