@misc{10481/70212,
year = {2020},
month = {12},
url = {http://hdl.handle.net/10481/70212},
abstract = {We prove existence and uniqueness of solutions to the initialboundary
value problem for the Lifshitz–Slyozov equation (a nonlinear transport
equation on the half-line), focusing on the case of kinetic rates with unbounded
derivative at the origin. Our theory covers in particular those cases
with rates behaving as power laws at the origin, for which an inflow behavior
is expected and a boundary condition describing nucleation phenomena needs
to be imposed. The method we introduce here to prove existence is based on a
formulation in terms of characteristics, with a careful analysis on the behavior
near the singular boundary. As a byproduct we provide a general theory for
linear continuity equations on a half-line with transport fields that degenerate
at the boundary. We also address both the maximality and the uniqueness of
inflow solutions to the Lifshitz–Slyozov model, exploiting monotonicity properties
of the associated transport equation.},
organization = {Spanish Government
European Commission	MTM2017-91054-EXP	
RTI2018-098850-B-IOO},
organization = {Plan Propio de Investigacion, Universidad de Granada, Programa 9 - partially through FEDER (ERDF) funds},
organization = {Junta de Andalucia
European Commission	P18-RT-2422	
A-FQM-311-UGR18},
organization = {Comision Nacional de Investigacion Cientifica y Tecnologica (CONICYT)
CONICYT FONDECYT	11170655},
publisher = {Institute of Physics Publishing},
keywords = {Nonlinear transport equation},
keywords = {Singular initial-boundary value problem},
keywords = {Dynamic boundary condition},
keywords = {Characteristics formulation},
keywords = {Oswald ripening},
keywords = {Nucleation theory},
keywords = {Polymerization},
title = {The initial-boundary value problem for the Lifshitz–Slyozov equation with non-smooth rates at the boundary},
doi = {10.1088/1361-6544/abd3f3},
author = {Calvo Yagüe, Juan and Hingant, Erwan and Yvinec, Romain},
}