| 具有空变系数的半线性反应-扩散抛物系统在非线性边界条件下解的爆破时间的下界 |
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| 引用本文： | 欧阳柏平,肖胜中.具有空变系数的半线性反应-扩散抛物系统在非线性边界条件下解的爆破时间的下界[J].数学的实践与认识,2021(7):226-233. |
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| 作者姓名： | 欧阳柏平 肖胜中 |
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| 作者单位： | 广州华商学院数据科学学院;广东农工商职业技术学院 |
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| 基金项目： | 广东省普通高校创新团队项目(2020WCXTD008);广东省普通高校重点项目(自然科学)(2019KZDXM042);广东财经大学华商学院校内项目(2020HSDS01) |
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| 摘 要： | 研究了高维空间上具有空变系数的半线性反应-扩散抛物系统在非线性边界条件下的解的爆破问题.构造了一个能量表达式,运用微分不等式的方法,得到了该能量方程所满足的微分不等式.然后通过积分导出了解的爆破时间下界的估计.
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| 关 键 词： | 爆破时间 非线性边界条件 下界 抛物系统 高维空间 空变系数 |
Lower Bound for the Blow-up Time of Quasi-Linear Reaction-Diffusion Parabolic Systems with Space Dependent Coefficients under Nonlinear Boundary Conditions |
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| OUYANG Bai-ping,XIAO Sheng-zhong.Lower Bound for the Blow-up Time of Quasi-Linear Reaction-Diffusion Parabolic Systems with Space Dependent Coefficients under Nonlinear Boundary Conditions[J].Mathematics in Practice and Theory,2021(7):226-233. |
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| Authors: | OUYANG Bai-ping XIAO Sheng-zhong |
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| Institution: | (College of Data Science,Guangzhou Huashang College,Guangzhou,511300,China;Guangdong AIB Polytechnic College,Guangzhou 510507,China) |
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| Abstract: | In this paper,we study the blow up phenomenon for quasi-linear reaction-diffusion parabolic systems with space dependent coefficients under nonlinear boundary conditions in high dimensional spaces.We formulate an energy expression.Using the technique of a differential inequality,we conclude that the energy satisfies a differential inequality.Then,by integrating the inequality,we derive the lower bound estimates of blow up time. |
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| Keywords: | blow-up time nonlinear boundary condition lower bound parabolic system high dimensional space space dependent coefficients |
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