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

ZHANF An-lei, LIU Bing-chen

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

Chinese Quarterly Journal of Mathematics >

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

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2025.01.007

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

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