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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 Giga
A 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 Analysis

ISSN

0036-1410

Issue

4

Volume

34

Page range

861-881

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2007-03-16

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