具有变系数和记忆边界流的抛物型方程的爆破解

doi:10.13371/j.cnki.chin.q.j.m.2025.01.007

数学季刊 ›› 2025, Vol. 40 ›› Issue (1): 74-81.doi: 10.13371/j.cnki.chin.q.j.m.2025.01.007

具有变系数和记忆边界流的抛物型方程的爆破解

College of Science, China University of Petroleum, Qingdao 266580, China

收稿日期:2021-03-17 出版日期:2025-03-30 发布日期:2025-03-30
通讯作者: 刘丙辰 E-mail:bcliu@upc.edu.cn
作者简介:ZHANG An-lei (1999-), female, native of Weifang, Shandong, student of China University of Petroleum, engages in control theory of differential equation; LIU Bing-chen (1976-), male, native of Weifang, Shandong, associate professor of China University of Petroleum, engages in partial differetial equation.
基金资助:
Supported by Shandong Provincial Natural Science Foundation (Grant Nos. ZR2021MA003 and ZR2020MA020).

Blow-Up Solutions in a Parabolic Equation with Variable Coefficients and Memory Boundary Flux

College of Science, China University of Petroleum, Qingdao 266580, China

Received:2021-03-17 Online:2025-03-30 Published:2025-03-30
Contact: LIU Bing-chen E-mail:bcliu@upc.edu.cn
About author:ZHANG An-lei (1999-), female, native of Weifang, Shandong, student of China University of Petroleum, engages in control theory of differential equation; LIU Bing-chen (1976-), male, native of Weifang, Shandong, associate professor of China University of Petroleum, engages in partial differetial equation.
Supported by:
Supported by Shandong Provincial Natural Science Foundation (Grant Nos. ZR2021MA003 and ZR2020MA020).

摘要/Abstract

摘要： This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions. We give the blow-up criteria for all nonnegative nontrivial solutions, which rely on the behavior of the coefficients when time variable tends to positive infinity. Moreover, the global existence of solutions are discussed for non-positive exponents.

关键词: Semilinear parabolic equation, Nonlinear memory boundary flux, Variable coefficient, Blow-up

Abstract: This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions. We give the blow-up criteria for all nonnegative nontrivial solutions, which rely on the behavior of the coefficients when time variable tends to positive infinity. Moreover, the global existence of solutions are discussed for non-positive exponents.

Key words: Semilinear parabolic equation, Nonlinear memory boundary flux, Variable , coefficient, Blow-up

中图分类号:

O175.26

张安蕾, 刘丙辰. 具有变系数和记忆边界流的抛物型方程的爆破解[J]. 数学季刊, 2025, 40(1): 74-81.

ZHANF An-lei, LIU Bing-chen. Blow-Up Solutions in a Parabolic Equation with Variable Coefficients and Memory Boundary Flux[J]. Chinese Quarterly Journal of Mathematics, 2025, 40(1): 74-81.

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具有变系数和记忆边界流的抛物型方程的爆破解

Blow-Up Solutions in a Parabolic Equation with Variable Coefficients and Memory Boundary Flux

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