A model for an electropaint process. (English) Zbl 0547.35048

Aitchison, J. M.; Lacey, A. A.; Shillor, M.

IMA J. Appl. Math. 33, 17-31 (1984).

Authors’ summary: A simple time-dependent model is proposed for the process of painting a metal surface by electrodeposition. The problem is then to solve the Laplace equation in a given region with a free boundary on a part of its surface. A related steady problem is considered. Numerical solutions to examples of both problems are presented. We also discuss the existence and regularity of the solutions to the steady problem and find the exact solution to a one-dimensional unsteady problem. In certain cases we are able to derive approximate solutions for other unsteady problems.

Reviewer: J.Rojtberg

MSC:

35J65	Nonlinear boundary value problems for linear elliptic equations
35R35	Free boundary problems for PDEs
35J25	Boundary value problems for second-order elliptic equations
65M99	Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99	Numerical methods for partial differential equations, boundary value problems
35A05	General existence and uniqueness theorems (PDE) (MSC2000)

Keywords:

model; painting; electrodeposition; Laplace equation; free boundary; Numerical solutions; existence; regularity; steady problem; exact solution; unsteady problem