一类分数阶(p,q)一Laplace扩散模型的爆破硏究
Blow-Up Analysis for a Class of Fractional (p,q)-Laplacian Diffusion Models
DOI: 10.12677/PM.2026.166153, PDF,    科研立项经费支持
作者: 陈程科*, 林强：长沙理工大学数学与统计学院，湖南长沙
关键词: 抛物方程；（p；q)-Laplace算子；爆破；Parabolic Equations； (p；q)-Laplacian； Blow-Up
摘要: 本文研究一类具分数阶(p，q)-Laplace算子的抛物方程在次临界初始能级下解的爆破行为。借助 凹函数方法与位势井理论，首先证得解的有限时间爆破；进而结合微分不等式技巧，给出爆破速率 估计。所得结果补充并完善了己有关于整体存在性与渐近行为的研究。
Abstract: This paper investigates the blow-up behavior of solutions to a class of parabolic equations involving fractional (p,q)-Laplace operators under subcritical initial energy level. By virtue of the concave function method and potential well theory, we first establish the finite time blow-up of solutions. Furthermore, we derive blow-up rate estimates via differential inequality techniques. The obtained results complement and enrich existing studies on global existence and asymptotic behavior.
文章引用：陈程科, 林强. 一类分数阶(p,q)一Laplace扩散模型的爆破硏究[J]. 理论数学, 2026, 16(6): 24-35. https://doi.org/10.12677/PM.2026.166153

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