| 带梯度项的椭圆型方程边界爆破解的高阶估计 |
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| 引用本文： | 张亚杰,马飞遥,沃维丰.带梯度项的椭圆型方程边界爆破解的高阶估计[J].数学研究及应用,2021,41(2):161-170. |
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| 作者姓名： | 张亚杰 马飞遥 沃维丰 |
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| 作者单位： | 宁波大学数学与统计学院, 浙江 宁波 315000 |
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| 基金项目： | 浙江省自然科学基金(Gran Nos.LY20A010010; LY20A010011), 国家自然科学基金(Grant No.11971251). |
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| 摘 要： | In this paper,the higher order asymptotic behaviors of boundary blow-up solutions to the equation■in bounded smooth domain■are systematically investigated for p and q.The second and third order boundary behaviours of the equation are derived.The results show the role of the mean curvature of the boundary■and its gradient in the high order asymptotic expansions of the solutions.
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| 关 键 词： | second order estimates third order estimates semilinear elliptic equations |
| 收稿时间： | 2020/3/24 0:00:00 |
| 修稿时间： | 2020/10/24 0:00:00 |
Higher Order Estimates for Boundary Blow-Up Solutions of Elliptic Equations with Gradient Term |
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| Yajie ZHANG,Feiyao MAO,Weifeng WO.Higher Order Estimates for Boundary Blow-Up Solutions of Elliptic Equations with Gradient Term[J].Journal of Mathematical Research with Applications,2021,41(2):161-170. |
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| Authors: | Yajie ZHANG Feiyao MAO Weifeng WO |
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| Institution: | Department of Mathematics, Ningbo University, Zhejiang 315000, P. R. China |
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| Abstract: | In this paper, the higher order asymptotic behaviors of boundary blow-up solutions to the equation $\Delta\,u={u}^{p}\pm |\nabla u|^{q}$ in bounded smooth domain $\Omega \subset {R}^{N} $ are systematically investigated for $p$ and $q$. The second and third order boundary behaviours of the equation are derived. The results show the role of the mean curvature of the boundary $\partial \Omega $ and its gradient in the high order asymptotic expansions of the solutions. |
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| Keywords: | second order estimates third order estimates semilinear elliptic equations |
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