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
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
Decay Rates of Weak Solutions to Non-Local Cauchy Problems
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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