期刊
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
卷 32, 期 10-12, 页码 1941-1964出版社
TAYLOR & FRANCIS INC
DOI: 10.1080/03605300701318955
关键词
aggregation; a priori estimates; backward diffusion; integro-differential equation; weak compactness
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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