Repository: Freie Universit├Ąt Berlin, Math Department

Properties of the solutions of delocalised coagulation and inception problems with outflow boundaries

Patterson, R. I. A (2016) Properties of the solutions of delocalised coagulation and inception problems with outflow boundaries. Journal of Evolution Equations, 16 . pp. 261-291.

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Well posedness is established for a family of equations modelling particle populations undergoing delocalised coagulation, advection, inflow and outflow in a externally specified velocity field. Very general particle types are allowed while the spatial domain is a bounded region of $d$-dimensional space for which every point lies on exactly one streamline associated with the velocity field. The problem is formulated as a semi-linear ODE in the Banach space of bounded measures on particle position and type space. A local Lipschitz property is established in total variation norm for the propagators (generalised semi-groups) associated with the problem and used to construct a Picard iteration that establishes local existence and global uniqueness for any initial condition. The unique weak solution is shown further to be a differentiable or at least bounded variation strong solution under smoothness assumptions on the parameters of the coagulation interaction. In the case of one spatial dimension strong differentiability is established even for coagulation parameters with a particular bounded variation structure in space. This one dimensional extension establishes the convergence of the simulation processes studied in [Patterson, Stoch. Anal. Appl. 31, 2013] to a unique and differentiable limit.

Item Type:Article
Additional Information:Preprint 02/2015:
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
ID Code:1896
Deposited By: Ulrike Eickers
Deposited On:12 Apr 2016 08:14
Last Modified:24 Oct 2017 12:56

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