A smooth solution for a Keldysh type equation

Journal Article · Mon Jul 01 00:00:00 EDT 1996 · Communications in Partial Differential Equations

DOI:https://doi.org/10.1080/03605309608821186· OSTI ID:255094

Canic, S ^[1]; Keyfitz, B L ^[2]

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1. Iowa State Univ., Ames, IA (United States)
2. Univ. of Houston, TX (United States)

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.

• Sponsoring Organization: USDOE
• OSTI ID: 255094
• Journal Information: Communications in Partial Differential Equations, Vol. 21, Issue 1-2; Other Information: PBD: 1996
• Country of Publication: United States
• Language: English

Related Subjects

99 MATHEMATICS
COMPUTERS
INFORMATION SCIENCE
MANAGEMENT
LAW
MISCELLANEOUS
PARTIAL DIFFERENTIAL EQUATIONS
DIRICHLET PROBLEM
BOUNDARY-VALUE PROBLEMS
ELLIPTICAL CONFIGURATION
NONLINEAR PROBLEMS