Journal
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
Volume 32, Issue 10-12, Pages 1941-1964Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/03605300701318955
Keywords
aggregation; a priori estimates; backward diffusion; integro-differential equation; weak compactness
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The purpose of this work is to develop a satisfactory existence theory for a general class of aggregation equations. An aggregation equation is a non-linear, non-local partial differential equation that is a regularization of a backward diffusion process. The non-locality arises via convolution with a potential. Depending on how regular the potential is, we prove either local or global existence for the solutions. Aggregation equations have been used recently to model the dynamics of populations in which the individuals attract each other (Bodnar and Velazquez, 2005; Holm and Putkaradze, 2005; Mogilner and Edelstein-Keshet, 1999; Morale et al., 2005; Topaz and Bertozzi, 2004; Topaz et al., 2006).
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