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Elliott, Charles Martin, Goto, S and Giga, Y (2003) Dynamic boundary conditions for Hamilton-Jacobi equations. SIAM Journal on Mathematical Analysis, 34 (4). pp. 861-881. ISSN 0036-1410
Full text not available from this repository.Abstract
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.
| Item Type: | Article |
|---|---|
| Keywords: | Hamilton--Jacobi equation, Dynamic boundary condition, Viscosity solution |
| Schools and Departments: | School of Mathematical and Physical Sciences > Mathematics |
| Subjects: | Q Science > QA Mathematics |
| Depositing User: | Charles Martin Elliott |
| Date Deposited: | 16 Mar 2007 |
| Last Modified: | 09 Sep 2019 14:00 |
| URI: | http://sro.sussex.ac.uk/id/eprint/893 |
| Google Scholar: | 3 Citations |