Neumann边界条件下非局部扩散方程解的爆破

Blow-up of solutions for a nonlocal diffusion system with Neumann boundary

处理了新Neumann边界条件下和带有反应项的非局部扩散的爆破问题。证明了问题解存在的唯一性,建立了比较原理。得到问题解的临界指标p*=1,当且仅当p>1时,非负非平凡的解在有限时刻爆破;反之,当p≤1时,每个解都是全局存在的。

The blow-up problem of the nonlocal diffusion system with new Neumann boundary and a reaction term is solved.We prove that the solution is unique,and build up a comparison principle.In addition,the critical exponent of solution p＊=1 is obtained.The non-negative and non-trivial solution blows up in a fixed time if and only if p1,while every solution is global if p≤1.