A note on Smoluchowski's equations with diffusion
We consider an infinite system of reaction-diffusion equations that models aggregation of particles. Under suitable assumptions on the diffusion coefficients and aggregation rates, we show that this system can be reduced to a scalar equation, for which an explicit self-similar solution is obtained. In addition, pointwise bounds for the solutions of associated initial and initial-boundary value problems are provided.
Please refer to publisher version or contact your library.