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具非局部源多孔介质方程的爆破

Blow-up for a Porous Medium Equation with Non-local Sources
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摘要 考虑带有齐次Dirichlet边界条件且具有非局部源项的多孔介质方程正解的爆破性质.在适当条件下,建立了该问题解的局部存在性,证明解在有限时刻爆破,并得到了该问题解的一致爆破模式. This paper deals with the blow-up properties of positive solutions to a porous medium equation with non-local sources,subject to null Dirichlet boundary conditions.With appropriate hypotheses,the local existence of the solution was first established,and then the finite time blow-up proved and meanwhile the uniform blow-up profiles obtained in the interior.
作者 蒋良军
机构地区 南京晓庄学院数学与信息技术学院
出处 《南京晓庄学院学报》 2010年第3期9-15,共7页 Journal of Nanjing Xiaozhuang University
基金 江苏省高校自然科学基金(09KJD110008)
关键词 多孔介质方程 非局部源 一致爆破模式. a porous medium equation nonlocal sources uniform blow-up profiles
分类号 O175.26 [理学—基础数学]
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参考文献10

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二级参考文献5

  • 1Ph. Souplet, Blow up in nonlocal reaction-diffusion equations, SIAM J. Math. Anal., 1998, 29: 1301-1334.
  • 2Ph. Souplet, Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source, J. Diff. Eqns., 1999, 153: 374-406.
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  • 4Anderson J. R., Local existence and uniqueness of solutions of degenerate parabolic equations, Comm. Partial Differential Equations, 1991, 16: 105-143.
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共引文献10

南京晓庄学院学报
2010年 第3期

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