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Front propagation for the aggregation-diffusion-reaction equation v τ = [D(v)vx]x + f(v) is investigated, where f is a bi-stable reaction-term and D(v) is a diffusion coefficient with changing sign, modeling aggregating-diffusing processes. We provide necessary and sufficient conditions for the existence of traveling wave solutions and classify them according to how or if they attain their equilibria at finite times. We also show that the dynamics can exhibit the phenomena of finite speed of propagation and/or finite speed of saturation. © World Scientific Publishing Company.

Original publication

DOI

10.1142/S0218202507002303

Type

Journal article

Journal

Mathematical Models and Methods in Applied Sciences

Publication Date

01/09/2007

Volume

17

Pages

1351 - 1368