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

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

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

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

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Abstract

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Abstract:

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.

Key words: fractional $p$ -Laplacian, Galerkin approximation, the solutions for global existence, differential inequality, blow-up

CLC Number:

O175.23

Jianjun Li,Yangchen Li. The Existence and Blow-Up of Solutions for a Class of Fractional $p$ -Laplace Diffusion Equation with Logarithmic Nonlinearity[J].Acta mathematica scientia,Series A, 2025, 45(2): 465-478.

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