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| 一类燃烧型的对流扩散方程解的定性性质 |
| Qualitative Properties of Solutions for a Class of Combustion Convection Diffusion Equations |
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| DOI：10.16018/j.cnki.cn32-1650/n.202104011 |
| 中文关键词: 反应—对流—扩散方程 自由边界 燃烧型非线性项 零点性质 |
| 英文关键词: reaction-convection-diffusion equation free boundary combustion type nonlinear term zero point property |
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| 中文摘要: |
| 研究具有燃烧型非线性项的反应—对流—扩散方程的自由边界问题，主要考虑在不同对流强度下解的渐近行为。利用相平面分析的方法对问题的平衡解进行分类，把对流的强度分成小对流和大对流两种情形。在两种对流强度下，问题具有完全不同的平衡解分类。对于大对流情形，构造合适的上解得到解在极限区间I∞上局部一致收敛于0；在小对流情形，利用ω-极限集以及零点性质，得到解在I∞上局部一致且收敛于0或1。 |
| 英文摘要: |
| In this paper, the free boundary of reactive-convection-diffusion equations with combustion nonlinear terms is studied,and the approaching behavior of solution under different convective intensity is mainly considered. We use phase plane analysis to classify the balance solution of the problem and divide the strength of convection into two situations: small convection and large convection. At these two convection intensity, the problem has a completely different balanced classification. For large convection situations, we construct a suitable upper solution on the limit range of I∞ locally consistent convergence to 0. In a small convection situation, we use the ω-limit set and zero-point nature to get the solution on the I∞ locally consistent convergence at 0 or 1. |
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