Journal ArticleDOI
Stationary and non-stationary patterns of the density-suppressed motility model
Manjun Ma,Rui Peng,Zhi-An Wang +2 more
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In this paper, Liu et al. showed that the DSM model does not admit non-constant steady states if either the chemical diffusion rate or the intrinsic growth rate of bacteria is large.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 2020-01-15. It has received 41 citations till now.read more
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Global dynamics and spatio-temporal patterns of predator-prey systems with density-dependent motion
Hai Yang Jin,Zhi-An Wang +1 more
TL;DR: In this article, the authors investigate the global boundedness, asymptotic stability and pattern formation of predator-prey systems with density-dependent prey-taxis in a two-dimensional bounded domain with Neumann boundary conditions.
Journal ArticleDOI
Boundedness and asymptotics of a reaction-diffusion system with density-dependent motility
TL;DR: In this article, the authors considered the initial-boundary value problem of a system of reaction-diffusion equations with density-dependent motility and proved that the problem has a unique classical global solution uniformly bounded in time.
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.
Journal ArticleDOI
Steady states and pattern formation of the density-suppressed motility model
Zhi-An Wang,Xin Xu +1 more
TL;DR: In this article, the authors considered the stationary problem of density-suppressed motility models in one dimension with Neumman boundary conditions and derived conditions on the existence of non-constant stationary solutions.
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Global classical solutions for a class of reaction-diffusion system with density-suppressed motility
Wenbin Lyu,Zhi-An Wang +1 more
TL;DR: In this paper, the authors considered a class of reaction-diffusion systems with density-suppressed motility and showed that the global solution admits a unique global classical solution for all nonnegative initial data.
References
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Book
Elliptic Partial Differential Equations of Second Order
David Gilbarg,Neil S. Trudinger +1 more
TL;DR: In this article, Leray-Schauder and Harnack this article considered the Dirichlet Problem for Poisson's Equation and showed that it is a special case of Divergence Form Operators.
Book ChapterDOI
Elliptic Partial Differential Equations of Second Order
Piero Bassanini,Alan R. Elcrat +1 more
TL;DR: In this paper, a class of partial differential equations that generalize and are represented by Laplace's equation was studied. And the authors used the notation D i u, D ij u for partial derivatives with respect to x i and x i, x j and the summation convention on repeated indices.
Book
Topics in Nonlinear Functional Analysis
TL;DR: Topological approach: Finite dimensions Topological degree in Banach space Bifurcation theory Further topological methods Monotone operators and the min-max theorem Generalized implicit function theorems Bibliography as mentioned in this paper
Journal ArticleDOI
Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues
TL;DR: In this article, a survey and critical analysis focused on a variety of chemotaxis models in biology, namely the classical Keller-Segel model and its subsequent modifications, which, in several cases, have been developed to obtain models that prevent the non-physical blow up of solutions.
Journal ArticleDOI
Diffusion, Self-Diffusion and Cross-Diffusion
Yuan Lou,Wei Ming Ni +1 more
TL;DR: In this paper, the authors proposed a mathematical model for spatial segregation of interacting species, where u1 and u2 represent the densities of two competing species, d1 and d2 are their diffu- sion rates, a1 and a2 denote the intrinsic growth rates, b1 and c2 account for intra specific competitions, b2 and c1 are the coefficients of inter-specific competitions, :11 and :22 are usually referred as selfdiffusion pressures, and :12 and :21 are cross-diffusion pressure.
Related Papers (5)
Boundedness, stabilization, and pattern formation driven by density-suppressed motility
Effects of signal-dependent motilities in a Keller–Segel-type reaction–diffusion system
Youshan Tao,Michael Winkler +1 more