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A sufficient condition of sensitivity functions for boundedness of solutions to a parabolic-parabolic chemotaxis system
Kentarou Fujie,Takasi Senba +1 more
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In this article, the authors considered the parabolic system as a perturbation of a nonlocal parabolic equation and established a sufficient condition of the sensitivity function χ for the global existence of solutions under the assumption of smallness of the constant τ.Abstract:
This paper deals with time-global solutions to the parabolic system under the homogeneous Neumann boundary conditions in a bounded and convex domain () with smooth boundary . Here τ is a positive parameter, χ is a smooth function on satisfying and is a pair of nonnegative initial data. We will consider the above system as a perturbation of a nonlocal parabolic equation and establish a sufficient condition of the sensitivity function χ for the global existence of solutions under the assumption of smallness of the constant τ.read more
Citations
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Journal ArticleDOI
A logarithmic chemotaxis model featuring global existence and aggregation
TL;DR: In this paper, the global existence of a chemotaxis model for cell aggregation phenomenon is obtained, which belongs to the class of logarithmic models and takes a Fokker-Planck type diffusion for the equation of cell density.
Journal ArticleDOI
Comparison methods for a Keller–Segel-type model of pattern formations with density-suppressed motilities
Kentarou Fujie,Jie Jiang +1 more
TL;DR: In this paper, an explicit point-wise upper bound for the degeneracy of a fully parabolic system was obtained, which showed that the classical solution always exists globally and remains uniformly-in-time bounded in the sub-critical case, while in the supercritical case a blowup may take place in infinite time rather than finite time.
Journal ArticleDOI
Classical solutions to a logistic chemotaxis model with singular sensitivity and signal absorption
Elisa Lankeit,Johannes Lankeit +1 more
TL;DR: In this article, the authors prove global existence of classical solutions to a chemotaxis system slightly generalizing u t = Δ u − χ ∇ ⋅ ( u v ∇ v ) + κ u − μ u 2 v t in a bounded domain Ω ⊂ R n, with homogeneous Neumann boundary conditions and for widely arbitrary positive initial data.
Journal ArticleDOI
Global Existence and Boundedness of Solutions to a Chemotaxis-Consumption Model with Singular Sensitivity
TL;DR: In this paper, the zero-flux chemotaxis system was studied in a smooth and bounded domain, and the existence of global classical solutions was shown in the presence of constant variance.
Posted Content
Boundedness of Classical Solutions to a Degenerate Keller--Segel Type Model with Signal-dependent Motilities
Kentaro Fujie,Jie Jiang +1 more
TL;DR: In this article, the authors considered the initial Neumann boundary value problem for a degenerate kinetic model of Keller-Segel type and proved that the classical solution is globally bounded if the motility function decreases slower than an exponential speed at high signal concentrations.
References
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Book
Geometric Theory of Semilinear Parabolic Equations
TL;DR: The neighborhood of an invariant manifold near an equilibrium point is a neighborhood of nonlinear parabolic equations in physical, biological and engineering problems as mentioned in this paper, where the neighborhood of a periodic solution is defined by the invariance of the manifold.
Journal ArticleDOI
Initiation of slime mold aggregation viewed as an instability.
Evelyn Fox Keller,Lee A. Segel +1 more
TL;DR: A mathematical formulation of the general interaction of amoebae, as mediated by acrasin is presented, and a detailed analysis of the aggregation process is provided.
Book
Nonlinear Potential Theory of Degenerate Elliptic Equations
TL;DR: In this paper, the existence of solutions for the obstacle problem is investigated and the John-Nirenberg lemma is shown to be true for nonlinear potential theory with respect to a super-harmonic function.
Book
Superlinear Parabolic Problems: Blow-up, Global Existence and Steady States
Pavol Quittner,Philippe Souplet +1 more
TL;DR: In this article, the authors propose a model for solving the model elliptic problems and model parabolic problems. But their model is based on Equations with Gradient Terms (EGS).
Journal ArticleDOI
Aggregation vs. global diffusive behavior in the higher-dimensional Keller–Segel model
TL;DR: In this article, the authors considered the classical parabolic-parabolic Keller-Segel system with homogeneous Neumann boundary conditions in a smooth bounded domain and proved that for each q > n 2 and p > n one can find e 0 > 0 such that if the initial data ( u 0, v 0 ) satisfy L q ( Ω ) e and ∇ v 0 ‖ L p (Ω) e then the solution is global in time and bounded and asymptotically behaves like the solution of a discoupled system of linear parabolic
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Initiation of slime mold aggregation viewed as an instability.
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