skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: A smooth solution for a Keldysh type equation

Abstract

We solve the Dirichlet problem for a nonlinear degenerate elliptic equation that arises in modeling weak shock reflection at a wedge. The equation exhibits a nonlinear version of a degeneracy first studied by Keldysh. Using monotone operator techniques, we prove existence of a weak solution in a weighed Sobolev space. For negative boundary data, the solution is smooth up to the degenerate boundary. By contrast, we showed in that positive boundary data lead to solutions with unbounded gradients at the degenerate boundary.

Authors:
 [1];  [2]
  1. Iowa State Univ., Ames, IA (United States)
  2. Univ. of Houston, TX (United States)
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
255094
Resource Type:
Journal Article
Journal Name:
Communications in Partial Differential Equations
Additional Journal Information:
Journal Volume: 21; Journal Issue: 1-2; Other Information: PBD: 1996
Country of Publication:
United States
Language:
English
Subject:
99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; PARTIAL DIFFERENTIAL EQUATIONS; DIRICHLET PROBLEM; BOUNDARY-VALUE PROBLEMS; ELLIPTICAL CONFIGURATION; NONLINEAR PROBLEMS

Citation Formats

Canic, S, and Keyfitz, B L. A smooth solution for a Keldysh type equation. United States: N. p., 1996. Web. doi:10.1080/03605309608821186.
Canic, S, & Keyfitz, B L. A smooth solution for a Keldysh type equation. United States. https://doi.org/10.1080/03605309608821186
Canic, S, and Keyfitz, B L. 1996. "A smooth solution for a Keldysh type equation". United States. https://doi.org/10.1080/03605309608821186.
@article{osti_255094,
title = {A smooth solution for a Keldysh type equation},
author = {Canic, S and Keyfitz, B L},
abstractNote = {We solve the Dirichlet problem for a nonlinear degenerate elliptic equation that arises in modeling weak shock reflection at a wedge. The equation exhibits a nonlinear version of a degeneracy first studied by Keldysh. Using monotone operator techniques, we prove existence of a weak solution in a weighed Sobolev space. For negative boundary data, the solution is smooth up to the degenerate boundary. By contrast, we showed in that positive boundary data lead to solutions with unbounded gradients at the degenerate boundary.},
doi = {10.1080/03605309608821186},
url = {https://www.osti.gov/biblio/255094}, journal = {Communications in Partial Differential Equations},
number = 1-2,
volume = 21,
place = {United States},
year = {Mon Jul 01 00:00:00 EDT 1996},
month = {Mon Jul 01 00:00:00 EDT 1996}
}