NDLI: Generalizing the Keller–Segel Model: Lyapunov Functionals, Steady State Analysis, and Blow-Up Results for Multi-species Chemotaxis Models in the Presence of Attraction and Repulsion Between Competitive Interacting Species

Please wait, while we are loading the content...

Generalizing the Keller–Segel Model: Lyapunov Functionals, Steady State Analysis, and Blow-Up Results for Multi-species Chemotaxis Models in the Presence of Attraction and Repulsion Between Competitive Interacting Species

Dynamics of Coupled Cell Networks: Synchrony, Heteroclinic Cycles and Inflation

Journal of Nonlinear Science : Volume 21, Issue 1, February 2011

Journal of Nonlinear Science : Volume 20

Journal of Nonlinear Science : Volume 19

Journal of Nonlinear Science : Volume 18

Journal of Nonlinear Science : Volume 17

Journal of Nonlinear Science : Volume 16

Journal of Nonlinear Science : Volume 15

Journal of Nonlinear Science : Volume 14

Journal of Nonlinear Science : Volume 13

Journal of Nonlinear Science : Volume 12

Journal of Nonlinear Science : Volume 11

Journal of Nonlinear Science : Volume 10

Journal of Nonlinear Science : Volume 9

Journal of Nonlinear Science : Volume 8

Journal of Nonlinear Science : Volume 7

Generalizing the Keller–Segel Model: Lyapunov Functionals, Steady State Analysis, and Blow-Up Results for Multi-species Chemotaxis Models in the Presence of Attraction and Repulsion Between Competitive Interacting Species

Content Provider	Springer Nature Link
Author	Horstmann, Dirk
Copyright Year	2010
Abstract	In this paper we extend the famous Keller–Segel model for the chemotactic movement of motile species to some multi-species chemotaxis equations. The presented multi-species chemotaxis models are more general than those introduced so far and also include some interaction effects that have not been studied before. For example, we consider multi-species chemotaxis models with attraction and repulsion between interacting motile species. For some of the presented new models we give sufficient conditions for the existence of Lyapunov functionals. These new results are related to those of Wolansky (Scent and sensitivity: equilibria and stability of chemotactic systems in the absence of conflicts, preprint, 1998; Eur. J. Appl. Math. 13:641–661, 2002). Furthermore, a linear stability analysis is performed for uniform steady states, and results for the corresponding steady state problems are established. These include existence and nonexistence results for non-constant steady state solutions in some special cases.
Ending Page	270
Page Count	40
Starting Page	231
File Format	PDF
ISSN	09388974
e-ISSN	14321467
Journal	Journal of Nonlinear Science
Issue Number	2
Volume Number	21
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-11-17
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Attraction ApplicationMathematics/Computational Methods of Engineering Initial-boundary value problems for second-order parabolic equations Repulsion Theoretical, Mathematical and Computational Physics Multi-species chemotaxis models Blow-up Asymptotic behavior of solutions Lyapunov functionals Analysis Steady state analysis Mechanics Economic Theory Cell movement (chemotaxis, etc.) Nonlinear parabolic equations
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Engineering Modeling and Simulation

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Remarks on finite-time blow-up in a fully parabolic attraction-repulsion chemotaxis system via reduction to the Keller-Segel system

Pattern formation of the attraction-repulsion keller-segel system.

On Chemotaxis Models with Cell Population Interactions

Global stabilization of the full attraction-repulsion Keller-Segel system

Blow-up profiles in quasilinear fully parabolic Keller--Segel systems

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

Finite-time blow-up in the three-dimensional fully parabolic attraction-dominated attraction-repulsion chemotaxis system

Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions $n\ge 3$

On the optimality of upper estimates near blow-up in quasilinear Keller--Segel systems

Generalizing the Keller–Segel Model: Lyapunov Functionals, Steady State Analysis, and Blow-Up Results for Multi-species Chemotaxis Models in the Presence of Attraction and Repulsion Between Competitive Interacting Species

Similar Documents

Remarks on finite-time blow-up in a fully parabolic attraction-repulsion chemotaxis system via reduction to the Keller-Segel system

Pattern formation of the attraction-repulsion keller-segel system.

On Chemotaxis Models with Cell Population Interactions

Global stabilization of the full attraction-repulsion Keller-Segel system

Blow-up profiles in quasilinear fully parabolic Keller--Segel systems

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

Finite-time blow-up in the three-dimensional fully parabolic attraction-dominated attraction-repulsion chemotaxis system

Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions $n\ge 3$

On the optimality of upper estimates near blow-up in quasilinear Keller--Segel systems

Generalizing the Keller–Segel Model: Lyapunov Functionals, Steady State Analysis, and Blow-Up Results for Multi-species Chemotaxis Models in the Presence of Attraction and Repulsion Between Competitive Interacting Species