在線閱讀 --自然科學版 2021年3期《具有Robin邊界條件的退化方程的爆破現象》
具有Robin邊界條件的退化方程的爆破現象--[在線閱讀]
李遠飛1, 石金誠1, 肖勝中2
1. 廣東財經大學 華商學院 數據科學學院, 廣東 廣州 511300;
2. 廣東農工商職業技術學院 科研處, 廣東 廣州 510507
起止頁碼: 217--223頁
DOI: 10.13763/j.cnki.jhebnu.nse.202101008
摘要
考慮了經常被用于模擬湍流過濾現象的退化拋物方程.運用微分不等式,對初始條件進行一些必要限制之后,得到了Robin邊界條件下解的爆破時間的下界以及確保解全局存在的條件.最后,證明了齊次Neumann邊界條件下解一定在某個有限時刻發生爆破,并得到了爆破時間的上界.

Blow-up Phenomenon of Degenerate Equations with Robin Boundary Condition
LI Yuanfei1, SHI Jincheng1, XIAO Shengzhong2
1. School of Data Science, Huashang College, Guangdong University of Finance & Economics, Guangdong Guangzhou 511300, China;
2. Research Administration, Guangdong AIB Polytechnic College, Guangdong Guangzhou 510507, China
Abstract:
The degenerate parabolic equation,which is often used to simulate turbulent filtration,is considered.By using differential inequality,the lower bound of the blow-up time of the solution under Robin boundary condition and the conditions to ensure the global existence of the solution are obtained.Finally,we prove that the solution must blow-up at a finite time under homogeneous Neumann boundary condition,and obtain the upper bound of blow-up time.

收稿日期: 2020-09-10
基金項目: 廣東省普通高校創新團隊項目(2020WCXTD008)

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