期刊
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
卷 45, 期 17, 页码 11683-11713出版社
WILEY
DOI: 10.1002/mma.8475
关键词
classical solution to PDEs; fractional partial differential equations; pointwise persistence; time-space logistic source; uniform persistence
资金
- Graduate Research and Innovation Projects of Jiangsu Province [KYCX21-3187]
- National Natural Science Foundation of China [11771380]
- Natural Science Foundation of Jiangsu Province [BK20191436]
In this paper, we study the fractional parabolic-elliptic Keller-Segel system with a time-space dependent logistic source. We prove the local existence and uniqueness of nonnegative classical solutions, as well as the global existence and boundedness of classical solutions under certain parameter conditions. We also find the pointwise persistence phenomena and uniform persistence phenomena of the solutions.
In this paper, we consider the following fractional parabolic-elliptic Keller-Segel system with time-space dependent logistic source on the whole space { u(t) + (-Delta)(s)u+chi del . (u del v) = u(a(t, x) - b(t,x)u), t > 0, x is an element of R-N, 0 = Delta v - lambda v + mu u, t > 0, x is an element of R-N, where s is an element of (0,1), chi, lambda and mu are positive constants and the functions a(t,x) and b(t,x) are positive and bounded. When the order of fractional diffusion s is an element of (1/2,1) and the functions a(t,x) and b(t,x) satisfy some conditions, we first prove the local existence and uniqueness of nonnegative classical solutions (u(t,x; t(0), u(0)), v(t,x; t(0), u(0))) with u(t(0),x; t(0), u(0)) = u(0) for every t(0) is an element of R and every nonnegative bounded and uniformly continuous initial function uo. Next, under some parameter conditions, we prove the global existence and boundedness of classical solutions (u(t,x; t(0), u(0)), v(t,x; t(0), u(0))) for given initial function u(0). Finally, we obtain the pointwise persistence phenomena of solutions; that is, for any strictly positive initial function u(0), there are 0 < m(u(0)) <= M(u(0)) < infinity such that m(u(0)) <= u(t,x; t(0), u(0)) <= M(u(0)), for all t >= 0, x is an element of R-N, and obtain the uniform persistence phenomena of solutions; that is, there are 0 < m < M < infinity such that for any strictly positive initial function u(0), there exists T(u(0)) > 0 such that m <= u(t, x; t(0), u(0)) <= M, for all t >= T(u(0)), x is an element of R-N, In summary, these results are extension to the case of fractional parabolic-elliptic Keller-Segel system.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据