Local and Global Existence for an Aggregation Equation |
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Authors: | Thomas Laurent |
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Institution: | 1. Department of Mathematics , Duke University , Durham, North Carolina, USA laurent@math.ucla.edu |
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Abstract: | 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
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Keywords: | Aggregation A priori estimates Backward diffusion Integro-differential equation Weak compactness |
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