Global existence and boundedness in an attraction-repulsion chemotaxis system with nonlocal logistic source and sublinear productions
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866915570957418496 |
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| author | Shanmugasundaram, Gnanasekaran Nagarajan, Nithyadevi |
| author_facet | Shanmugasundaram, Gnanasekaran Nagarajan, Nithyadevi |
| contents | This paper deals with the following attraction-repulsion chemotaxis system with nonlocal logistic source and sublinear productions \[ \left\{ \begin{array}{rrll} &&u_t = d_1 Δu-χ\nabla\cdot(u^k \nabla v)+ξ\nabla\cdot(u^k \nabla w)+ μu^m \left(1-\int_Ωu(x,t){\rm d}x\right),\qquad &x\inΩ,\, t>0,\\ &&v_t = d_2 Δv-αv+f(u), &x\inΩ,\, t>0,\\ &&w_t = d_3 Δw-βw+f(u), &x\inΩ,\, t>0,\\ &&\frac{\partial u}{\partialν} = \frac{\partial v}{\partialν} = \frac{\partial w}{\partialν} = 0, &x\in\partialΩ,\, t>0,\\ &&u(x,0) = u_0, \quad v(x,0)=v_0, \quad w(x,0)=w_0,&x\inΩ, \end{array} \right. \] in an open, bounded domain $Ω\subset \mathbb{R}^n$, $n\geq 2$ with smooth boundary $\partialΩ$. Assume the parameters $d_1$, $d_2$, $d_3$, $χ$, $ξ$, $α$, $β$ and $μ$ are positive constants, initial data $(u_0, v_0, w_0)$ are nonnegative and the function $f(u)\leq K u^l\in C^1([0, \infty))$ for some $K, l>0$. Under appropriate conditions on the parameter $k$, $l$ and $m$ we show that the above problem admits a unique globally bounded classical solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08305 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global existence and boundedness in an attraction-repulsion chemotaxis system with nonlocal logistic source and sublinear productions Shanmugasundaram, Gnanasekaran Nagarajan, Nithyadevi Analysis of PDEs 35A01, 35A09, 92C17, 37N25 This paper deals with the following attraction-repulsion chemotaxis system with nonlocal logistic source and sublinear productions \[ \left\{ \begin{array}{rrll} &&u_t = d_1 Δu-χ\nabla\cdot(u^k \nabla v)+ξ\nabla\cdot(u^k \nabla w)+ μu^m \left(1-\int_Ωu(x,t){\rm d}x\right),\qquad &x\inΩ,\, t>0,\\ &&v_t = d_2 Δv-αv+f(u), &x\inΩ,\, t>0,\\ &&w_t = d_3 Δw-βw+f(u), &x\inΩ,\, t>0,\\ &&\frac{\partial u}{\partialν} = \frac{\partial v}{\partialν} = \frac{\partial w}{\partialν} = 0, &x\in\partialΩ,\, t>0,\\ &&u(x,0) = u_0, \quad v(x,0)=v_0, \quad w(x,0)=w_0,&x\inΩ, \end{array} \right. \] in an open, bounded domain $Ω\subset \mathbb{R}^n$, $n\geq 2$ with smooth boundary $\partialΩ$. Assume the parameters $d_1$, $d_2$, $d_3$, $χ$, $ξ$, $α$, $β$ and $μ$ are positive constants, initial data $(u_0, v_0, w_0)$ are nonnegative and the function $f(u)\leq K u^l\in C^1([0, \infty))$ for some $K, l>0$. Under appropriate conditions on the parameter $k$, $l$ and $m$ we show that the above problem admits a unique globally bounded classical solution. |
| title | Global existence and boundedness in an attraction-repulsion chemotaxis system with nonlocal logistic source and sublinear productions |
| topic | Analysis of PDEs 35A01, 35A09, 92C17, 37N25 |
| url | https://arxiv.org/abs/2507.08305 |