Blow-Up Behaviors of Solutions to Reaction-Diffusion Equations With Nonlocal Sources and Variable Exponents北大核心CSCD

该文考虑了一类带有变指数非局部项的反应扩散方程的爆破问题。首先，由不动点原理，证明了问题解的局部存在性和唯一性。其次，利用上下解方法，给出在齐次Dirichlet边界条件下，问题的解在有限时间发生爆破的充分条件，即变指数大于零且初始值足够大，并对爆破时间的上下界进行了估计。

Blow-Up Behaviors of Solutions to Reaction-Diffusion Equations With Nonlocal Sources and Variable Exponents

The blow-up problems of the solutions are considered for reaction-diffusion equations with nonlocal sources and variable exponents. Firstly, the local existence and uniqueness of solutions to the problem were proved under the fixed-point theorem. Secondly, by means of the super- and sub-solution method, some sufficient conditions for the occurrence of finite-time blow-up were determined under the homogeneous Dirichlet boundary conditions, i.e., the variable exponent is positive and the initial value is large enough. Moreover, the estimates of upper and lower bounds of the blow-up time were given.