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| 摘要: |
| 本文研究了具有非线性非局部边界条件的一类退化型多孔介质方程. 利用比较原理和上下解的方法, 获得了方程的解是否在有限时刻爆破或整体存在的准则, 这些结果表明, 权重函数g(x, y)及指数l的大小对于问题解的爆破与否起着关键的作用. 最后研究了爆破解的爆破率. |
| 关键词: 多孔介质方程 非线性非局部边界条件 整体存在 爆破 爆破率 |
| DOI： |
| 分类号:O175.26 |
| 基金项目:Supported by National Natural Science Foundation of China (11461076) and Universities and colleges research foundation of Guangxi(ZD2014106). |
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| GLOBAL EXISTENCE AND BLOW-UP FOR A NONLINEAR POROUS MEDIUM EQUATION WITH NONLINEAR NONLOCAL BOUNDARY CONDITION |
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LING Zheng-qiu
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| Abstract: |
| This paper studies a degenerate nonlinear porous medium equation ut = Δum + aup∫Ωuqdx with nonlinear and nonlocal boundary condition u|∂Ω×(0,∞)= ∫Ωg(x, y)ul(y, t)dy. With the help of the comparison principle and super-, sub-solution methods, some criteria on this problem which determine whether the solutions blow up in a finite time or the solutions exist for all time are given. These results show that the global existence and blow-up results depend on the weight function g(x, y) and the size of l. Finally, the blow-up rate of the blow-up solutions is given. |
| Key words: porous medium equation nonlinear nonlocal boundary condition global exis-tence blow-up blow-up rate |
