Local and Global Solutions Near Equilibria via the Energy Method

2017 ◽  
pp. 1-91
Author(s):  
Jan Burczak ◽  
Yoshihiro Shibata ◽  
Wojciech M. Zaja̧czkowski
Keyword(s):  
Energy Method ◽  
Global Solutions ◽  
Local And Global Solutions

scholarly journals Problem solving in MNCs: How local and global solutions are (and are not) created

2012 ◽  
Vol 43 (8) ◽  
pp. 746-771 ◽  
Author(s):  
Esther Tippmann ◽  
Pamela Sharkey Scott ◽  
Vincent Mangematin
Keyword(s):  
Problem Solving ◽  
Global Solutions ◽  
Local And Global Solutions

scholarly journals Taking Perturbation to the Accuracy Frontier: A Hybrid of Local and Global Solutions

2012 ◽  
Vol 42 (3) ◽  
pp. 307-325 ◽  
Author(s):  
Lilia Maliar ◽  
Serguei Maliar ◽  
Sébastien Villemot
Keyword(s):  
Global Solutions ◽  
Local And Global Solutions

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

2019 ◽  
Vol 29 (08) ◽  
pp. 1465-1509
Author(s):  
Francesca Romana Guarguaglini ◽  
Marco Papi ◽  
Flavia Smarrazzo
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Elliptic System ◽  
Global Solutions ◽  
Transmission Conditions ◽  
The Other ◽  
Density Functions ◽  
Biological Models ◽  
Local And Global Solutions ◽  
Elliptic Model

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 [Formula: see text]-norm) initial data — as well as their uniqueness.

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