Level set method for solving Poisson's equation with discontinuous nonlinearities
Date
2005-11-25
Authors
Kolibal, Joseph
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
We study semi-linear elliptic free boundary problems in which the forcing term is discontinuous; i.e., a Poisson's equation where the forcing term is the Heaviside function applied to the unknown minus a constant. This approach uses level sets to construct a monotonic sequence of iterates which converge to a class of solutions to the free boundary problem. The monotonicity of the construction based on nested sets provides insight into the connectivity of the free boundary sets associated with the solutions.
Description
Keywords
Laplace equation, Reduced wave equation (Helmholtz), Poisson equation, Nonlinear elliptic PDE
Citation
Kolibal, J. (2005). Level set method for solving Poisson's equation with discontinuous nonlinearities. <i>Electronic Journal of Differential Equations, 2005</i>(132), pp. 1-12.
Rights
Attribution 4.0 International