一类带有时变系数的分数阶扩散方程解的爆破性

Abstract

Abstract:

In this paper, the blow-up properties of solutions for a class of fractional diffusion equations with time dependent coefficients is studied. By means of the potential well theory, Nehari manifold, concave conex method, and various differential inequalities, the finite time blow-up of the solutions under subcritical initial energy level, negative initial energy level and any positive initial energy level is discussed.And the upper bound of blow-up time is obtained.In particular, due to the energy functional and the depth of the potential well are related to the time-dependent coefficient $f(t)$ , in the case of sub-critical initial energy level, the upper bound of blow-up time will change with $f(t)$ .

Key words: Fractional, Time-dependent coefficient, Potential well, Blow-up

CLC Number:

O175.2

Gao Xiaoru, Li Jianjun, Tu Jun. Blow-Up of Solutions for a Class of Fractional Diffusion Equations with Time Dependent Coefficients[J].Acta mathematica scientia,Series A, 2024, 44(5): 1230-1241.

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Blow-Up of Solutions for a Class of Fractional Diffusion Equations with Time Dependent Coefficients

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