非线性边界条件下高维抛物方程解的全局存在性及爆破现象

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非线性边界条件下高维抛物方程解的全局存在性及爆破现象李远飞广东财经大学华商学院, 广州 Blow-up Phenomena and Global Existences for Higher-dimensional Parabolic Equations Under Nonlinear Boundary Conditions LI YuanfeiHuashang College, Guangdong University of Finance and Economics, Guangzhou 511300, China

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摘要该文研究了非线性边界条件下高维空间上更一般化的非线性抛物问题解的爆破现象以及全局解的存在性.通过构造辅助函数，并对方程中的已知数据项进行一些必要的假设，应用微分不等式技术，当爆破发生时推导了爆破时间的下界.也推到了方程的解一定发生的条件并得到了爆破时间的上界.同时，不管方程对外施力还是受到外力的作用，也研究了方程的解全局存在的条件.

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收稿日期: 2018-04-02

PACS:

O175.29

基金资助:广东省高等教育2017年"创新强校"专项资金（HS2018CXQX24）资助项目.

引用本文:

李远飞. 非线性边界条件下高维抛物方程解的全局存在性及爆破现象[J]. 应用数学学报, 2019, 42(6): 721-735. LI Yuanfei. Blow-up Phenomena and Global Existences for Higher-dimensional Parabolic Equations Under Nonlinear Boundary Conditions. Acta Mathematicae Applicatae Sinica, 2019, 42(6): 721-735.

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http://123.57.41.99/jweb_yysxxb/CN/或 http://123.57.41.99/jweb_yysxxb/CN/Y2019/V42/I6/721

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