4.7 Article

On the strongly competitive case in a fully parabolic two-species chemotaxis system with Lotka-Volterra competitive kinetics

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Mathematics, Applied

ON A QUASILINEAR FULLY PARABOLIC TWO-SPECIES CHEMOTAXIS SYSTEM WITH TWO CHEMICALS

Xu Pan et al.

Summary: This paper discusses a two-species chemotaxis system with nonlinear diffusion, sensitivity, signal secretion, and logistic source. It establishes the global boundedness of solutions under specific conditions and analyzes the large-time behavior of smooth bounded solutions.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B (2022)

Article Mathematics, Applied

Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision

N. Bellomo et al.

Summary: This paper focuses on exotic chemotaxis and cross-diffusion models in complex environments, discussing their derivation, characteristics, and potential new models. It also examines analytical problems in applying these models to real-world dynamics and explores research perspectives in a multiscale vision.

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES (2022)

Article Mathematics, Applied

Keller-Segel Chemotaxis Models: A Review

Gurusamy Arumugam et al.

Summary: In this paper, we review and discuss important methods and blow-up criteria for analyzing solutions of Keller-Segel chemotaxis models, discussing results on global existence, boundedness, and blow-up of solutions to different types of models. The numerical analysis of these models is still in its early stages, with known results on numerical methods and open problems in the field also highlighted.

ACTA APPLICANDAE MATHEMATICAE (2021)

Article Mathematics, Applied

Global solvability and asymptotic behavior in a two-species chemotaxis system with Lotka-Volterra competitive kinetics

Guoqiang Ren et al.

Summary: This work addresses a two-species chemotaxis system with Lotka-Volterra competitive kinetics in a bounded domain with smooth boundary. It constructs weak solutions and shows that they become smooth after a certain waiting time, and studies the asymptotic behavior of the solutions. The results generalize some well-known results in the literature.

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES (2021)

Article Mathematics, Applied

Stabilization in a two dimensional two-species aerotaxis-Navier-Stokes system

Eunji Jeong et al.

Summary: This study focuses on the two-species aerotaxis-Navier-Stokes equations with Lotka-Volterra competitive kinetics in a two-dimensional domain, considering general chemotactic sensitivity functions and oxygen consumption rate functions. The research results in the stabilization of the solution to the system, with global stabilization observed under specific conditions regarding chemotactic sensitivity and initial data, when the competition between two species is stronger than that within each species.

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS (2021)

Article Mathematics, Applied

Boundedness in a two-species chemotaxis system with nonlinear sensitivity and signal secretion

Xu Pan et al.

Summary: This study investigates a fully parabolic two-species chemotaxis system with nonlinear sensitivity and signal secretion. It is proven that the system has a global bounded classical solution under different parameter conditions when the initial data satisfy appropriate regularization assumptions. This work partially builds on results reported by Ren and Liu (2019) [22].

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2021)

Article Mathematics, Applied

BOUNDEDNESS AND ASYMPTOTIC STABILITY IN A QUASILINEAR TWO-SPECIES CHEMOTAXIS SYSTEM WITH NONLINEAR SIGNAL PRODUCTION

Xu Pan et al.

Summary: This paper investigates the global bounded smooth solution of a quasilinear two-species chemotaxis system under specific conditions, partially improving existing results. Moreover, when certain parameters are met, the global bounded solution of the system exponentially converges to specific values.

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS (2021)

Article Mathematics

Global existence and asymptotic behavior in a two-species chemotaxis system with logistic source

Guoqiang Ren et al.

JOURNAL OF DIFFERENTIAL EQUATIONS (2020)

Article Mathematics, Applied

Boundedness in a three-dimensional two-species chemotaxis system with two chemicals

Xu Pan et al.

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK (2020)

Article Mathematics, Applied

IncImprovement of conditions for boundedness in a two-species chemotaxis competition system of parabolic-parabolic-elliptic type

Liangchen Wang

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2020)

Article Mathematics, Applied

Boundedness in a three-dimensional two-species and two-stimuli chemotaxis system with chemical signalling loop

Xu Pan et al.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2020)

Article Mathematics, Applied

On a fully parabolic chemotaxis system with Lotka-Volterra competitive kinetics

Xie Li et al.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2019)

Article Mathematics, Applied

Boundedness and stabilization in a two-species chemotaxis-competition system of parabolic-parabolic-elliptic type

Masaaki Mizukami

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2018)

Article Mathematics, Applied

How strong a logistic damping can prevent blow-up for the minimal Keller-Segel chemotaxis system?

Tian Xiang

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2018)

Article Mathematics, Applied

On the weakly competitive case in a two-species chemotaxis model

Tobias Black et al.

IMA JOURNAL OF APPLIED MATHEMATICS (2016)

Article Mathematics

Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics

Michael Winkler et al.

INDIANA UNIVERSITY MATHEMATICS JOURNAL (2016)

Article Mathematics, Applied

BOUNDEDNESS VS. BLOW-UP IN A TWO-SPECIES CHEMOTAXIS SYSTEM WITH TWO CHEMICALS

Youshan Tao et al.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B (2015)

Article Mathematics

Asymptotic stability of a two species chemotaxis system with non-diffusive chemoattractant

Mihaela Negreanu et al.

JOURNAL OF DIFFERENTIAL EQUATIONS (2015)

Article Mathematics, Applied

Boundedness in a two-species chemotaxis system

Ke Lin et al.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2015)

Article Mathematics, Applied

Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues

N. Bellomo et al.

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES (2015)

Article Mathematics, Applied

Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis-fluid system

Youshan Tao et al.

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK (2015)

Article Mathematics, Applied

Global boundedness of solutions to a two-species chemotaxis system

Qingshan Zhang et al.

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK (2015)

Article Mathematics, Applied

Nondegeneracy of blow-up points for the parabolic Keller-Segel system

Noriko Mizoguchi et al.

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE (2014)

Article Biology

Competitive exclusion in a two-species chemotaxis model

C. Stinner et al.

JOURNAL OF MATHEMATICAL BIOLOGY (2014)

Article Mathematics, Applied

ON A TWO SPECIES CHEMOTAXIS MODEL WITH SLOW CHEMICAL DIFFUSION

Mihaela Negreanu et al.

SIAM JOURNAL ON MATHEMATICAL ANALYSIS (2014)

Article Mathematics, Applied

Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system

Michael Winkler

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES (2013)

Article Mathematics

Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity

Youshan Tao et al.

JOURNAL OF DIFFERENTIAL EQUATIONS (2012)

Article Mathematics, Applied

Stabilization in a two-species chemotaxis system with a logistic source

J. I. Tello et al.

NONLINEARITY (2012)

Article Mathematics, Applied

Boundedness in the Higher-Dimensional Parabolic-Parabolic Chemotaxis System with Logistic Source

Michael Winkler

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS (2010)

Review Microbiology

Bacterial competition: surviving and thriving in the microbial jungle

Michael E. Hibbing et al.

NATURE REVIEWS MICROBIOLOGY (2010)

Article Biology

A user's guide to PDE models for chemotaxis

T. Hillen et al.

JOURNAL OF MATHEMATICAL BIOLOGY (2009)

Article Mathematics

Boundedness vs. blow-up in a chemotaxis system

D Horstmann et al.

JOURNAL OF DIFFERENTIAL EQUATIONS (2005)

Article Mathematics, Applied

The one-dimensional chemotaxis model: global existence and asymptotic profile

T Hillen et al.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2004)

Article Mathematics, Applied

Multi-components chemotactic system in the absence of conflicts

G Wolansky

EUROPEAN JOURNAL OF APPLIED MATHEMATICS (2002)

Article Mathematics, Applied

Blow-up in a chemotaxis model without symmetry assumptions

D Horstmann et al.

EUROPEAN JOURNAL OF APPLIED MATHEMATICS (2001)