Blow-up of solutions for nonlocal diffusion equations with a weighted gradient reaction
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摘要: 研究了加权梯度反应非局部扩散方程解的爆破现象, 并且给出了解存在和爆破的充分条件. 首先利用Banach不动点定理证明解的局部存在性; 其次利用特征函数构造了一个新的辅助函数; 最后结合微分不等式技巧得到了爆破时间的上界.Abstract: This paper considers the blow-up phenomena of solutions for nonlocal diffusion equations with a weighted gradient reaction, and gives the sufficient conditions for existence and blow-up. Firstly, the local existence of solutions is proven by using the Banach fixed-point theorem. Secondly, a new auxiliary function is constructed by using eigenfunctions. Finally, the results are combined with the differential inequality technique to obtain the upper bound of the blow-up time.
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Key words:
- weight function /
- gradient reaction /
- nonlocal diffusion /
- blow-up
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