Details
| Original language | English |
|---|---|
| Article number | 608 |
| Journal | NONLINEARITY |
| Volume | 35 |
| Issue number | 1 |
| Publication status | Published - 6 Jan 2022 |
| Externally published | Yes |
Abstract
Systems of the type can be used to model pursuit-evasion relationships between predators and prey. Apart from local kinetics given by f 1 and f 2, the key components in this system are the taxis terms -∇ ⋅ (S 1(u)∇v) and +∇ ⋅ (S 2(v)∇u); that is, the species are not only assumed to move around randomly in space but are also able to partially direct their movement depending on the nearby presence of the other species. In the present article, we construct global weak solutions of (∗) for certain prototypical nonlinear functions D i , S i and f i , i ∈ {1, 2}. To that end, we first make use of a fourth-order regularisation to obtain global solutions to approximate systems and then rely on an entropy-like identity associated with (∗) for obtaining various a priori estimates.
Keywords
- 35B45, 35D30, 35K59, 92C17 (secondary), double cross-diffusion, predator-prey, pursuit-evasion, weak solutions Mathematics Subject Classification numbers: 35K51 (primary)
ASJC Scopus subject areas
- Physics and Astronomy(all)
- General Physics and Astronomy
- Mathematics(all)
- Applied Mathematics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Mathematical Physics
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In: NONLINEARITY, Vol. 35, No. 1, 608, 06.01.2022.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Global weak solutions to fully cross-diffusive systems with nonlinear diffusion and saturated taxis sensitivity
AU - Fuest, Mario
N1 - Publisher Copyright: © 2021 IOP Publishing Ltd & London Mathematical Society.
PY - 2022/1/6
Y1 - 2022/1/6
N2 - Systems of the type can be used to model pursuit-evasion relationships between predators and prey. Apart from local kinetics given by f 1 and f 2, the key components in this system are the taxis terms -∇ ⋅ (S 1(u)∇v) and +∇ ⋅ (S 2(v)∇u); that is, the species are not only assumed to move around randomly in space but are also able to partially direct their movement depending on the nearby presence of the other species. In the present article, we construct global weak solutions of (∗) for certain prototypical nonlinear functions D i , S i and f i , i ∈ {1, 2}. To that end, we first make use of a fourth-order regularisation to obtain global solutions to approximate systems and then rely on an entropy-like identity associated with (∗) for obtaining various a priori estimates.
AB - Systems of the type can be used to model pursuit-evasion relationships between predators and prey. Apart from local kinetics given by f 1 and f 2, the key components in this system are the taxis terms -∇ ⋅ (S 1(u)∇v) and +∇ ⋅ (S 2(v)∇u); that is, the species are not only assumed to move around randomly in space but are also able to partially direct their movement depending on the nearby presence of the other species. In the present article, we construct global weak solutions of (∗) for certain prototypical nonlinear functions D i , S i and f i , i ∈ {1, 2}. To that end, we first make use of a fourth-order regularisation to obtain global solutions to approximate systems and then rely on an entropy-like identity associated with (∗) for obtaining various a priori estimates.
KW - 35B45
KW - 35D30
KW - 35K59
KW - 92C17 (secondary)
KW - double cross-diffusion
KW - predator-prey
KW - pursuit-evasion
KW - weak solutions Mathematics Subject Classification numbers: 35K51 (primary)
UR - http://www.scopus.com/inward/record.url?scp=85123542923&partnerID=8YFLogxK
U2 - 10.1088/1361-6544/ac3922
DO - 10.1088/1361-6544/ac3922
M3 - Article
VL - 35
JO - NONLINEARITY
JF - NONLINEARITY
SN - 0951-7715
IS - 1
M1 - 608
ER -