Level set method for solving Poisson's equation with discontinuous nonlinearities

Level set method for solving Poisson's equation with discontinuous nonlinearities

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...

Full description

Bibliographic Details
Main Author: Joseph Kolibal
Format: Article
Language:English
Published: Texas State University 2005-11-01
Series:Electronic Journal of Differential Equations
Subjects:
Laplace equation
reduced wave equation (Helmholtz)
Poisson equation
nonlinear elliptic PDE.
Online Access:http://ejde.math.txstate.edu/Volumes/2005/132/abstr.html
id doaj-aa9c7225174f44158823d8251b41c0db
record_format Article
spelling doaj-aa9c7225174f44158823d8251b41c0db2020-11-24T23:44:12ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912005-11-012005132112Level set method for solving Poisson's equation with discontinuous nonlinearitiesJoseph KolibalWe 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. http://ejde.math.txstate.edu/Volumes/2005/132/abstr.htmlLaplace equationreduced wave equation (Helmholtz)Poisson equationnonlinear elliptic PDE.
collection DOAJ
language English
format Article
sources DOAJ
author Joseph Kolibal
spellingShingle Joseph Kolibal
Level set method for solving Poisson's equation with discontinuous nonlinearities
Electronic Journal of Differential Equations
Laplace equation
reduced wave equation (Helmholtz)
Poisson equation
nonlinear elliptic PDE.
author_facet Joseph Kolibal
author_sort Joseph Kolibal
title Level set method for solving Poisson's equation with discontinuous nonlinearities
title_short Level set method for solving Poisson's equation with discontinuous nonlinearities
title_full Level set method for solving Poisson's equation with discontinuous nonlinearities
title_fullStr Level set method for solving Poisson's equation with discontinuous nonlinearities
title_full_unstemmed Level set method for solving Poisson's equation with discontinuous nonlinearities
title_sort level set method for solving poisson's equation with discontinuous nonlinearities
publisher Texas State University
series Electronic Journal of Differential Equations
issn 1072-6691
publishDate 2005-11-01
description 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.
topic Laplace equation
reduced wave equation (Helmholtz)
Poisson equation
nonlinear elliptic PDE.
url http://ejde.math.txstate.edu/Volumes/2005/132/abstr.html
work_keys_str_mv AT josephkolibal levelsetmethodforsolvingpoissonsequationwithdiscontinuousnonlinearities
_version_ 1725499658585767936

Similar Items