在線閱讀 --自然科學版 2021年3期《具有位勢項的熱量方程解的全局存在性與爆破現象》
具有位勢項的熱量方程解的全局存在性與爆破現象--[在線閱讀]
李志青, 李遠飛, 李宗锎
廣東財經大學 華商學院 數據科學學院, 廣東 廣州 511300
起止頁碼: 231--238頁
DOI: 10.13763/j.cnki.jhebnu.nse.202101010
摘要
考慮了定義在ΩRNN ≥ 2)上的熱量方程utum-Vxu+upmp>1,當m+1>2p時,證明了解的全局存在性.若m<p,假設方程的初始數據滿足一定的約束條件,證明了方程的解在有限時刻一定發生爆破并獲得了爆破時間的上界.如果2 < N < 4p/2p-(m+1)且p < m+1 < 2p,或者N=2且p+1 < m+1 < 2p,確定了爆破時間的下界.

The Existence and the Blow-up Phenomenon of Solutions to the Heat Equation with Variable Coeffcients Under Nonlinear Boundary Conditions
LI Zhiqing, LI Yuanfei, LI Zongkai
School of Data Science, Huashang College, Guangdong University of Finance & Economics, Guangdong Guangzhou 511300, China
Abstract:
In this paper,the heat equation with variable coefficients defined on Ω is considered,in which ΩRN(N ≥ 2) is a bounded convex region and the equation has nonlinear boundary conditions.By using differential inequalities,we first derive the conditions under which the blow-up must occur and determine the upper bound of the blow-up time.Meanwhile,by making certain restrictions on the nonlinear terms,we also obtain the global existence of the solution.When the blow-up occurs,the lower bound of blasting time is also determined.

收稿日期: 2020-09-10
基金項目: 廣東省普通高校重點項目(自然科學)(2019KZDXM042);廣東財經大學華商學院校內導師制項目(2019HSDS23)

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