一类具有对数非线性源项的分数阶p-Laplace扩散方程解的存在性和爆破  

The Existence and Blow-Up of Solutions for a Class of Fractional p-Laplace Diffusion Equation with Logarithmic Nonlinearity

作　　者：李建军[1] 李阳晨 Li Jianjun;Li Yangchen(College of Science,Liaoning Technical University,Liaoning Fucin 123000)

机构地区：[1]辽宁工程技术大学理学院,辽宁阜新123000

出　　处：《数学物理学报(A辑)》2025年第2期465-478,共14页Acta Mathematica Scientia

摘　　要：该文研究了一类具有对数非线性源项的分数阶p-Laplace扩散方程的初边值问题.文中利用Galerkin近似、势阱理论和Nehari流形的方法证明了方程在亚临界状态和临界状态下解的全局存在性,然后通过构造辅助函数、应用微分不等式给出了解在有限时间内爆破的一些充分条件.The paper study the initial-boundary value problem for a class of fractional p-Laplace diffusion equation with logarithmic nonlinearity.Using the Galerkin approximation,potential well theory and Nehari manifold methods,the global existence of solutions in subcritical and critical states is proven.Then,by constructing auxiliary functions and applying differential inequality techniques,the existence of blow-up solutions in finite time is established.

关 键 词：分数阶p-Laplace方程 Galerkin近似 全局解 微分不等式 爆破 

分 类 号：O175.23[理学—数学]