Existence of solution for a system of repulsion and alignment: Comparison between theory and simulation

Thi-Bich-Ngoc  Mac

doi:10.3934/dcdsb.2015.20.3013

Article Contents

2015, Volume 20, Issue 9: 3013-3027. Doi: 10.3934/dcdsb.2015.20.3013

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Existence of solution for a system of repulsion and alignment: Comparison between theory and simulation

Thi-Bich-Ngoc Mac^1,

1.
1-Université de Toulouse; UPS, INSA, UT1, UTM, 2-CNRS, Institut de Mathématiques de Toulouse, F-31062 Toulouse

Received: June 30, 2014

Revised: April 30, 2015

Published: October 2015

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Abstract

This paper is devoted to study the existence of solutions of hydrodynamic model for systems of self-propelled particles subject to alignment and volume exclusion interactions. On one hand, we prove the existence of solutions by using the modified Garlerkin method for quasi-linear parabolic simulations. On the other hand, we also perform simulations to compare theoretical and numerical results. The numerical results show that the numerical solutions exist for short time in some cases of coefficients.

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Mathematics Subject Classification: 35Q80, 35L60, 82C22, 82C70, 92D50.

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