一类非局部扩散方程组解的爆破

研究一类非局部扩散方程组的解的性质,利用严格压缩映射和不动点理论可以验证该方程组的解的局部存在性.再通过比较原理,构造了爆破下解,从而证明方程组解的爆破性质,最后还给出了爆破时间的上界估计.

Blow-up for a nonlocal diffusion equations

In this paper we study some properties of a nonlocal diffusion equations. First, by the use of contraction mapping and the fixed point theory, we prove that the solutions of the system exist locally; then by constructing comparison lemma and lower solution, we obtain that the solutions blow up under some conditions, moreover, we derive the estimate of maximal existence time of blow up solutions from the upper bound.