Herrero, Miguel A. and Rodrigo, Marianito R. (2005) A note on Smoluchowski's equations with diffusion. Applied Mathematics Letters, 18 (9). pp. 969-975. ISSN 0893-9659
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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.
|Uncontrolled Keywords:||Particle aggregation; reaction-diffusion; explicit solutions; supersolution; subsolution; kpp-fisher equation; coagulation equations; kinetics; aggregation; existence; discrete; gelation; model; dynamics; behavior|
|Subjects:||Sciences > Mathematics > Differential equations|
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|Deposited On:||13 Sep 2012 10:38|
|Last Modified:||07 Feb 2014 09:27|
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