Blow-up and global existence for a kinetic equation of swarm formation

In the present paper we study possible blow–ups and global existence for a kinetic equation that describes swarm formations in the variable interacting rate case.

[1]  P. Degond,et al.  Local Stability of Perfect Alignment for a Spatially Homogeneous Kinetic Model , 2014, 1403.5233.

[2]  J. Carrillo,et al.  Double milling in self-propelled swarms from kinetic theory , 2009 .

[3]  Lorenzo Pareschi,et al.  Reviews , 2014 .

[4]  Massimo Fornasier,et al.  Particle, kinetic, and hydrodynamic models of swarming , 2010 .

[5]  M. Fila,et al.  Reaction versus diffusion: blow-up induced and inhibited by diffusivity , 2005 .

[6]  M. Lachowicz,et al.  A Kinetic Model for the formation of Swarms with nonlinear interactions , 2015 .

[7]  H. Othmer,et al.  Models of dispersal in biological systems , 1988, Journal of mathematical biology.

[8]  M. Lachowicz,et al.  Methods of Small Parameter in Mathematical Biology , 2014 .

[9]  Mirosław Lachowicz,et al.  Individually-based Markov processes modeling nonlinear systems in mathematical biology , 2011 .

[10]  Jacek Banasiak,et al.  On a macroscopic limit of a kinetic model of alignment , 2012, 1207.2643.

[11]  B. Perthame,et al.  Mathematik in den Naturwissenschaften Leipzig An Integro-Differential Equation Model for Alignment and Orientational Aggregation , 2007 .

[12]  Pierre Degond,et al.  Kinetic limits for pair-interaction driven master equations and biological swarm models , 2011, 1109.4538.

[13]  Martin Parisot,et al.  A simple kinetic equation of swarm formation: Blow-up and global existence , 2016, Appl. Math. Lett..

[14]  M. Stoll,et al.  Bifurcation analysis of an orientational aggregation model , 2003, Journal of mathematical biology.

[15]  Pavol Quittner,et al.  Superlinear Parabolic Problems , 2007, Birkhäuser Advanced Texts Basler Lehrbücher.

[16]  L. Pontryagin,et al.  Ordinary differential equations , 1964 .

[17]  Hans G. Othmer,et al.  The Diffusion Limit of Transport Equations Derived from Velocity-Jump Processes , 2000, SIAM J. Appl. Math..

[18]  Nicola Bellomo,et al.  Stochastic Evolving Differential Games Toward a Systems Theory of Behavioral Social Dynamics , 2015, 1506.05699.

[19]  S. Kaniel,et al.  The Boltzmann equation , 1978 .

[20]  조준학,et al.  Growth of human bronchial epithelial cells at an air-liquid interface alters the response to particle exposure , 2013, Particle and Fibre Toxicology.

[21]  Juan Soler,et al.  ON THE MATHEMATICAL THEORY OF THE DYNAMICS OF SWARMS VIEWED AS COMPLEX SYSTEMS , 2012 .

[22]  Hans G. Othmer,et al.  The Diffusion Limit of Transport Equations II: Chemotaxis Equations , 2002, SIAM J. Appl. Math..