数学季刊 >

2025 , Vol. 40 >Issue 1: 74 - 81

DOI: https://doi.org/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

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

收稿日期: 2021-03-17

  网络出版日期: 2025-03-30

基金资助

Supported by Shandong Provincial Natural Science Foundation (Grant Nos. ZR2021MA003 and ZR2020MA020).

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

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  • College of Science, China University of Petroleum, Qingdao 266580, China
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.
LIU Bing-chen (1976-), male, native of Weifang, Shandong, associate professor of China University of Petroleum, engages in partial differetial equation.

Received date: 2021-03-17

  Online published: 2025-03-30

Supported by

Supported by Shandong Provincial Natural Science Foundation (Grant Nos. ZR2021MA003 and ZR2020MA020).

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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

本文引用格式

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

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

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