Local and global solutions for a hyperbolic-elliptic model of chemotaxis on a network

被引：3

作者：

Guarguaglini, Francesca Romana ^{[1
]}

Papi, Marco ^{[2
]}

Smarrazzo, Flavia ^{[2
]}

机构：

[1] Univ Aquila, Dipartimento Ingn & Sci Informaz & Matemat, Via Vetoio, I-67100 Laquila, Italy

[2] Univ Campus Biomed Roma, Via Alvaro Portillo 21, I-00128 Rome, Italy

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2019年 / 29卷 / 08期

关键词：

Hyperbolic-elliptic systems; networks; transmission conditions; global existence of solutions; chemotaxis; BEHAVIOR; MIGRATION; STABILITY; SYSTEM;

D O I：

10.1142/S021820251950026X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study a hyperbolic-elliptic system on a network which arises in biological models involving chemotaxis. We also consider suitable transmission conditions at internal points of the graph which on one hand allow discontinuous density functions at nodes, and on the other guarantee the continuity of the fluxes at each node. Finally, we prove local and global existence of non-negative solutions - the latter in the case of small (in the L-1-norm) initial data - as well as their uniqueness.

引用

页码：1465 / 1509

页数：45

共 34 条

[1]

[Anonymous], 2014, SEMIGROUP METHODS EV

[2]

Bellomo N., 2017, T AM MATH SOC, V4, P31, DOI DOI 10.1090/BTRAN/17

[3] A degenerate chemotaxis system with flux limitation: Maximally extended solutions and absence of gradient blow-up [J].

Bellomo, Nicola ;

Winkler, Michael .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2017, 42 (03) :436-473

[4]

Boccardo L., 2013, DEGRUYTER STUDIES MA, V55

[5] THE SCALAR KELLER-SEGEL MODEL ON NETWORKS [J].

Borsche, R. ;

Goettlich, S. ;

Klar, A. ;

Schillen, P. .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2014, 24 (02) :221-247

[6] Flows on networks: recent results and perspectives [J].

Bressan, Alberto ;

Canic, Suncica ;

Garavello, Mauro ;

Herty, Michael ;

Piccoli, Benedetto .

EMS SURVEYS IN MATHEMATICAL SCIENCES, 2014, 1 (01) :47-111

[7] A HYPERBOLIC MODEL OF CHEMOTAXIS ON A NETWORK: A NUMERICAL STUDY [J].

Bretti, G. ;

Natalini, R. ;

Ribot, M. .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2014, 48 (01) :231-258

[8] Numerical approximation of nonhomogeneous boundary conditions on networks for a hyperbolic system of chemotaxis modeling the Physarum dynamics [J].

Bretti, Gabriella ;

Natalini, Roberto .

JOURNAL OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING, 2018, 18 (01) :85-115

[9] Parabolic models for chemotaxis on weighted networks [J].

Camilli, Fabio ;

Corrias, Lucilla .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2017, 108 (04) :459-480

[10]

Cazenave T., 1998, OXFORD LECT SERIES M, V13

← 1 2 3 4 →