Dynamic boundary conditions for Hamilton-Jacobi equations

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

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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
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