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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회지 대한수학회지 제58권 제5호
- 발행연도
- 2021.9
- 수록면
- 1,227 - 1,237 (11page)
- DOI
- 10.4134/JKMS.j200538
이용수
초록· 키워드
오류제보하기
This paper is concerned with a reaction-diffusion logistic model. In \cite{L06}, Lou observed that a heterogeneous environment with diffusion makes the total biomass greater than the total carrying capacity. Regarding the ratio of biomass to carrying capacity, Ni \cite{HN16} raised a conjecture that the ratio has a upper bound depending only on the spatial dimension. For the one-dimensional case, Bai, He, and Li \cite{BHL16} proved that the optimal upper bound is $3$. Recently, Inoue and Kuto \cite{IK20} showed that the supremum of the ratio is infinity when the domain is a multi-dimensional ball. In this paper, we generalized the result of \cite{IK20} to an arbitrary smooth bounded domain in $\mathbb{R}^n, n \geq 2$. We use the sub-solution and super-solution method. The idea of the proof is essentially the same as the proof of \cite{IK20} but we have improved the construction of sub-solutions. This is the complete answer to the conjecture of Ni.
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참고문헌 (21)
참고문헌 신청
X. Bai / 2016 / An optimization problem and its application in population dynamics / Proc. Amer. Math. Soc 144(5):2161~2170
Henri Berestycki / 2009 / Bistable traveling waves around an obstacle / Communications on Pure and Applied Mathematics 62(6):729~788
R. S. Cantrell / 2003 / Spatial ecology via reaction-diffusion equations, Wiley Se-ries in Mathematical and Computational Biology / John Wiley & Sons, Ltd
W. Ding / 2010 / Optimal control of growth coefficient on a steady-state population model / Nonlinear Analysis: Real World Applications 11(2):688~704
Jack Dockery / 1998 / The evolution of slow dispersal rates: a reaction diffusion model / Journal of Mathematical Biology 37(1):61~83
Henri Berestycki / 2009 / Bistable traveling waves around an obstacle / Communications on Pure and Applied Mathematics 62(6):729~788
R. S. Cantrell / 2003 / Spatial ecology via reaction-diffusion equations, Wiley Se-ries in Mathematical and Computational Biology / John Wiley & Sons, Ltd
W. Ding / 2010 / Optimal control of growth coefficient on a steady-state population model / Nonlinear Analysis: Real World Applications 11(2):688~704
Jack Dockery / 1998 / The evolution of slow dispersal rates: a reaction diffusion model / Journal of Mathematical Biology 37(1):61~83
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