Results 31 to 40 of about 895 (106)
On the weakly competitive case in a two-species chemotaxis model
, 2016 In this article we investigate a parabolic-parabolic-elliptic two-species chemotaxis system with weak competition and show global asymptotic stability of the coexistence steady state under a smallness condition on the chemotactic strengths, which seems ...
Black, Tobias +2 more
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Open MathematicsWe investigate the two-species chemotaxis predator-prey system given by the following system: ut=Δu−χ∇⋅(u∇w)+u(λ1−μ1ur1−1+av),x∈Ω,t>0,vt=Δv+ξ∇⋅(v∇z)+v(λ2−μ2vr2−1−bu),x∈Ω,t>0,0=Δw−w+v,x∈Ω,t>0,0=Δz−z+u,x∈Ω,t>0,\left\{\begin{array}{ll}{u}_{t}=\Delta u-\chi \
Liu Ling
doaj +1 more source
Depleting the signal: Analysis of chemotaxis-consumption models -- A survey [PDF]
arXiv, 2023 We give an overview of analytical results concerned with chemotaxis systems where the signal is absorbed. We recall results on existence and properties of solutions for the prototypical chemotaxis-consumption model and various variants and review more recent findings on its ability to support the emergence of spatial structures.
arxiv
Advances in Nonlinear AnalysisThe Keller-Segel-Navier-Stokes system in RN{{\mathbb{R}}}^{N} is considered, where N≥3N\ge 3. We show the existence and uniqueness of local mild solutions for arbitrary initial data and gravitational potential in scaling invariant Lorentz spaces ...
Takeuchi Taiki
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Some remarks on the solution of the cell growth equation [PDF]
arXiv, 2023 The analytical solution to the initial-boundary value problem for the cell growth equation was given in the paper Zaidi A. A., Van Brunt B., Wake G.C., Solutions to an advanced functional partial differential equation of the pantograph type, Proc. R. Soc. A 471: 20140947 (2015). In this note, we simplify the arguments given in the paper mentioned above
arxiv
Boundedness and exponential convergence of a chemotaxis model for tumor invasion
, 2016 We revisit the following chemotaxis system modeling tumor invasion \begin{equation*} \begin{cases} u_t=\Delta u-\nabla \cdot(u\nabla v),& x\in\Omega, t>0,\\ v_t=\Delta v+wz,& x\in\Omega, t>0,\\ w_t=-wz,& x\in\Omega, t>0,\\ z_t=\Delta z-z+u, & x\in\Omega,
Jin, Haiyang, Xiang, Tian
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Global existence of large solutions for the parabolic-elliptic Keller-Segel system in Besov type spaces [PDF]
arXiv, 2023 In this paper, we investigate global existence of large solutions for the parabolic-elliptic Keller-Segel system in the homogeneous Besov type spaces. A class of initial data was presented, generating a global smooth solution although the $\dot{B}^{-2}_{\infty,\infty}$-norm of the initial data may be chosen arbitrarily large.
arxiv
Sub-logistic source can prevent blow-up in the 2D minimal Keller-Segel chemotaxis system
, 2017 It is well-known that the Neumann initial-boundary value problem for the minimal-chemotaxis-logistic system in a 2D bounded smooth domain has no blow-up for any choice of parameters. Here, for a large class of kinetic terms including sub-logistic sources,
Xiang, Tian
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Global existence for a kinetic model of chemotaxis via dispersion and Strichartz estimates
, 2007 We investigate further the existence of solutions to kinetic models of chemotaxis. These are nonlinear transport-scattering equations with a quadratic nonlinearity which have been used to describe the motion of bacteria since the 80's when experimental ...
Bournaveas, Nikolaos +3 more
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Blow-up of weak solutions to a chemotaxis system under influence of an external chemoattractant
, 2015 We study nonnnegative radially symmetric solutions of the parabolic-elliptic Keller-Segel whole space system \begin{align*} \left\{\begin{array}{c@{\,}l@{\quad}l@{\,}c} u_{t}&=\Delta u-\nabla\!\cdot(u\nabla v),\ &x\in\mathbb{R}^n,& t>0,\\ 0 &=\Delta v+u ...
Black, Tobias
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