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Author Country (or Countries)

South Africa

Abstract

In this paper, existence and uniqueness of a global solution to continuous, non-common and non-linear convectioncoagulation equations are investigated by means of various techniques. The method of characteristics (Mizohata, 1973), substochastic methods and Kato-Voigt pertubation (Banasiak et al., 2006) are exploited to show that the linear operator (transport-coagulation ) is the infinitesimal generator of a strongly continuous semigroup. Then, uniqueness of the solution to the full nonlinear problem follows by showing that the coagulation term is globally Lipschitz, hereby addressing the problem of existence and uniqueness for the combined coagulation and transport processes.

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