林火南. 非局部柯西问题弱解的衰减速度[J]. 应用概率统计, 2017, 33(6): 642-654. DOI: 10.3969/j.issn.1001-4268.2017.06.007
引用本文: 林火南. 非局部柯西问题弱解的衰减速度[J]. 应用概率统计, 2017, 33(6): 642-654. DOI: 10.3969/j.issn.1001-4268.2017.06.007
shu
LIN HuoNan. Decay Rates of Weak Solutions to Non-Local Cauchy Problems[J]. Chinese Journal of Applied Probability and Statistics, 2017, 33(6): 642-654. DOI: 10.3969/j.issn.1001-4268.2017.06.007
Citation: LIN HuoNan. Decay Rates of Weak Solutions to Non-Local Cauchy Problems[J]. Chinese Journal of Applied Probability and Statistics, 2017, 33(6): 642-654. DOI: 10.3969/j.issn.1001-4268.2017.06.007
shu

非局部柯西问题弱解的衰减速度

Decay Rates of Weak Solutions to Non-Local Cauchy Problems

    摘要
  • 摘要: 考虑如(1)所示的非局部柯西问题弱解(u_t)_t\ge0的渐近性质.仅利用跳核J(x,y)当|x-y|充分大时下界的性质,本文证明了对于任意1\le q<p<\infty及充分大t,\|u_t\|_p\le c(t)\|u_0\|_q成立, 同时给出c(t)的最优显示估计式.

     

    Abstract: In this paper, the asymptotic behavior of the weak solution (u_t)_t\ge0 to the non-local Cauchy problems as stated in (1) is considered. Only using lower bounds of jumping kernel J(x,y) for large |x-y|, it is obtained that \|u_t\|_p\le c(t)\|u_0\|_q with any 1\le q<p<\infty and large t. Explicit and sharp formulas for c(t) are also given.

     

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