Blowup of Radial Solutions to a Parabolic-Elliptic System Related to Chemotaxis

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We study blowup of radial solutions to a parabolic-elliptic system related to a biological model. The model describes chemotactic aggregation of cellular slime molds which move preferentially towards relatively high concentrations of a chemical secreted by the amoebae themselves. We think that blowup of solutions to the system corresponds to chemotactic aggregation of the living things. In the model, the relation between the movement of cells and the chemical concentration is represented by the chemotaxis coefficient. The behavior of solutions is determined by the chemotaxis coefficient and the initial function. In the present paper, we investigate a sufficient condition for blowup of solutions to the system.
2011-03-31