# American Institute of Mathematical Sciences

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November  2015, 20(9): 3013-3027. doi: 10.3934/dcdsb.2015.20.3013

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

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

Received  July 2014 Revised  May 2015 Published  September 2015

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.
Citation: Thi-Bich-Ngoc Mac. Existence of solution for a system of repulsion and alignment: Comparison between theory and simulation. Discrete & Continuous Dynamical Systems - B, 2015, 20 (9) : 3013-3027. doi: 10.3934/dcdsb.2015.20.3013
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