A Note on Singularity Formation for a Nonlocal Transport Equation (Research)

2020 ◽  
pp. 227-242
Author(s):  
Vu Hoang ◽  
Maria Radosz
Keyword(s):  
Transport Equation ◽  
Singularity Formation ◽  
Nonlocal Transport

NUMERICAL TREATMENT OF A NONLINEAR NONLOCAL TRANSPORT EQUATION MODELING CRYSTAL PRECIPITATION

2008 ◽  
Vol 18 (09) ◽  
pp. 1505-1527 ◽  
Author(s):  
ROMINA GOBBI ◽  
SILVIA PALPACELLI ◽  
RENATO SPIGLER
Keyword(s):  
Differential Equations ◽  
Transport Equation ◽  
Communication Theory ◽  
Hyperbolic Partial Differential Equations ◽  
Equation Modeling ◽  
Method Of Solution ◽  
Delta Functions ◽  
Nonlocal Transport ◽  
Precipitation Phenomena ◽  
Initial Crystal

Numerical methods to solve certain nonlinear nonlocal transport equations (hyperbolic partial differential equations with smooth solutions), even singular at the boundary, are developed and analyzed. As a typical case, a model equation used to describe certain crystal precipitation phenomena (a slight variant of the so-called Lifshitz–Slyozov–Wagner model) is considered. Choosing a train of few delta functions as initial crystal size distribution, one can model the technologically important case of having only a modest number of crystal sizes. This leads to the reduction of the transport equation to a system of ordinary differential equations, and suggests a new method of solution for the transport equation, based on Shannon sampling, which is widely used in communication theory.

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