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Dynamic boundary conditions for Hamilton-Jacobi equations
journal contribution
posted on 2023-06-07, 13:52 authored by Charles Martin Elliott, S Goto, Y GigaA nonstandard dynamic boundary condition for a Hamilton--Jacobi equation in one space dimension is studied in the context of viscosity solutions. A comparison principle, and hence uniqueness, is proved by consideration of an equivalent notion of viscosity solution for an alternative formulation of the boundary condition. The relationship with a Neumann condition is established. Global existence is obtained by consideration of a related parabolic approximation with a dynamic boundary condition. The problem is motivated by applications in superconductivity and interface evolution.
History
Publication status
- Published
Journal
SIAM Journal on Mathematical AnalysisISSN
0036-1410External DOI
Issue
4Volume
34Page range
861-881Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2007-03-16Usage metrics
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