Existence and asymptotic behaviour for the time-fractional Keller-Segel model for chemotaxis
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DOI: 10.1002/mana.201700237
Abstract: One of the most important systems for understanding chemotactic aggregation is the Keller–Segel system. We consider the time‐fractional Keller–Segel system of order α∈(0,1). We prove an existence result with small initial data in a class… read more here.
Keywords: asymptotic behaviour; fractional keller; time fractional; keller ... See more keywords
Asymptotic behavior of solutions of a model derived from the 1-D Keller–Segel model on the half line
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DOI: 10.1002/mma.4189
Abstract: In this paper, we are interested in a model derived from the 1-D Keller-Segel model on the half line x > as follows: ut−lux−uxx=−β(uvx)x,x>0,t>0,λv−vxx=u,x>0,t>0,lu(0,t)+ux(0,t)=vx(0,t)=0,t>0,u(x,0)=u0(x),x>0, where l is a constant. Under the conserved boundary condition, we study… read more here.
Keywords: model derived; model half; half line; segel model ... See more keywords
Similarity Solutions for Keller‐Segel model with fractional diffusion of cells
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DOI: 10.1002/mma.6122
Abstract: In this paper, the similarity method has been used to solve fractional Keller‐Segel model where the diffusion is represented by a nonlocal fractional Laplace operator. In order to verify the results, fractional centred difference method… read more here.
Keywords: keller segel; solutions keller; diffusion; segel model ... See more keywords
Nonnegative solutions to time fractional Keller–Segel system
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DOI: 10.1002/mma.6880
Abstract: We establish the existence of nonnegative weak solutions to time fractional Keller–Segel system with Dirichlet boundary condition in a bounded domain with smooth boundary. Since the considered system has a cross‐diffusion term and the corresponding… read more here.
Keywords: keller segel; system; solutions time; segel system ... See more keywords
On the parabolic‐elliptic Keller–Segel system with signal‐dependent motilities: A paradigm for global boundedness and steady states
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DOI: 10.1002/mma.7455
Abstract: This paper is concerned with a parabolic‐elliptic Keller–Segel system where both diffusive and chemotactic coefficients (motility functions) depend on the chemical signal density. This system was originally proposed by Keller and Segel to describe the… read more here.
Keywords: keller segel; system; segel system; signal dependent ... See more keywords
Spatial Analyticity of Solutions to Keller–Segel Equation of Parabolic–Elliptic Type
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DOI: 10.1007/s00025-017-0741-1
Abstract: In this article, spatial analyticity of solutions to Keller–Segel equation of parabolic–elliptic type with generalized dissipation is presented. First, we prove the analyticity of local solutions to system with large rough initial data in Modulation… read more here.
Keywords: analyticity solutions; solutions keller; beta; spatial analyticity ... See more keywords
Global Boundedness of the Fully Parabolic Keller-Segel System with Signal-Dependent Motilities
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DOI: 10.1007/s10440-021-00392-8
Abstract: This paper establishes the global uniform-in-time boundedness of solutions to the following Keller-Segel system with signal-dependent diffusion and chemotaxis { u t = ∇ ⋅ ( γ ( v ) ∇ u − u ϕ… read more here.
Keywords: keller; segel system; keller segel; phi ... See more keywords
Finite element method for solving Keller–Segel chemotaxis system with cross-diffusion
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DOI: 10.1007/s40435-017-0335-5
Abstract: This paper presents a finite element method for nonlinear parabolic–parabolic system of partial differential equations, which describe the chemotactic features, called a Keller–Segel system with additional cross-diffusion term in the second equation. Firstly a semi-implicit… read more here.
Keywords: finite element; system; element method; cross diffusion ... See more keywords
Chemotaxis effect vs logistic damping on boundedness in the 2-D minimal Keller-Segel model
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DOI: 10.1016/j.crma.2018.07.002
Abstract: In this paper, we study chemotaxis effect vs logistic dampening on boundedness for the two-dimensional minimal Keller-Segel model with logistic source in a 2-D smooth and bounded domain. It is well-known that this model allows… read more here.
Keywords: chemotaxis effect; effect logistic; model; keller segel ... See more keywords
On mean-field limits and quantitative estimates with a large class of singular kernels: Application to the Patlak–Keller–Segel model
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DOI: 10.1016/j.crma.2019.09.007
Abstract: In this note, we propose a new relative entropy combination of the methods developed by P.--E. Jabin and Z.~Wang [Inventiones (2018)] and by S. Serfaty [Proc. Int. Cong. of Math, (2018) and references therein] to… read more here.
Keywords: mean field; segel model; patlak keller; quantitative estimates ... See more keywords
The variational formulation of the fully parabolic Keller–Segel system with degenerate diffusion
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DOI: 10.1016/j.jde.2017.03.020
Abstract: Abstract We prove the time-global existence of solutions of the degenerate Keller–Segel system in higher dimensions, under the assumption that the mass of the first component is below a certain critical value. What we deal… read more here.
Keywords: segel system; system; time; keller segel ... See more keywords