Existence and uniqueness of a weak solution of a nonlocal aggregation equation with degenerate diffusion of general form

Abstract

The uniqueness of a weak solution of a nonlocal aggregation equation with degenerate diffusion is proved using the method of energy estimates. The existence of a solution is proved by combining the methods of iterations and contraction maps with the use of energy estimates. The equations under consideration arise in models of biological aggregation. Bibliography: 23 titles.