The initial-boundary value problem for the Lifshitz–Slyozov equation with non-smooth rates at the boundary Calvo Yagüe, Juan Hingant, Erwan Yvinec, Romain Nonlinear transport equation Singular initial-boundary value problem Dynamic boundary condition Characteristics formulation Oswald ripening Nucleation theory Polymerization The authors would like to thank Boris Andreianov and Guy Barles (Institut Denis Poisson, Universit´e de Tours) for many interesting and helpful discussions on the subject. We also warmly thank the reviewers for their careful reading of the manuscript, and their valuable remarks that help us improve its quality. J. C. acknowledges support from MICINN, projects MTM2017-91054-EXP and RTI2018-098850-B-IOO; he also acknowledges support from Plan Propio de Investigaci ´on, Universidad de Granada, Programa 9 -partially through FEDER (ERDF) funds-. E. H. acknowledges support from FONDECYT Iniciaci´on n◦ 11170655. R. Y. does not have to thank the French National Research Agency for its financial support but he kindly thanks it for the excellent reviews embellished with arguments based on scientific and cultural novelties in the expertise of his yearly application file during the last four years. Part of this work was done while J. C. and R. Y. were visiting the Departamento de Matem´atica at Universidad del B´ıo-B´ıo and while E. H. and J. C. were visiting Institut Denis Poisson at Universit´e de Tours and INRAE Nouzilly. J.C. thanks Universit´e de Tours for a visiting position during last winter. 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. 2021-09-15T08:45:43Z 2021-09-15T08:45:43Z 2020-12-09 info:eu-repo/semantics/article Published version: Juan Calvo et al 2021 Nonlinearity 34 1975. [10.1088/1361-6544/abd3f3] http://hdl.handle.net/10481/70212 10.1088/1361-6544/abd3f3 eng http://creativecommons.org/licenses/by-nc-nd/3.0/es/ info:eu-repo/semantics/openAccess Atribución-NoComercial-SinDerivadas 3.0 España Institute of Physics Publishing