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Hokkaido University Preprint Series in Mathematics >
SINGULAR NEUMANN PROBLEMS AND LARGE-TIME BEHAVIOR OF SOLUTIONS OF NONCOERCIVE HAMILTON-JACOBI EQUATIONS
| Title: | SINGULAR NEUMANN PROBLEMS AND LARGE-TIME BEHAVIOR OF SOLUTIONS OF NONCOERCIVE HAMILTON-JACOBI EQUATIONS |
| Authors: | GIGA, YOSHIKAZU Browse this author | | LIU, QING Browse this author | | MITAKE, HIROYOSHI Browse this author |
| Issue Date: | 26-Oct-2010 |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 971 |
| Start Page: | 1 |
| End Page: | 39 |
| Abstract: | We investigate the large-time behavior of viscosity solutions of Hamilton- Jacobi equations with noncoercive Hamiltonian in a multidimensional Euclidean space. Our motivation comes from a model describing growing faceted crystals recently discussed by E. Yokoyama, Y. Giga and P. Rybka. Surprisingly, growth rates of viscosity solutions of these equations depend on x-variable. In a part of the space called the effective domain, growth rates are constant but outside of this domain, they seem to be unstable. Moreover, on the boundary of the effective domain, the gradient with respect to x-variable of solutions blows up as time goes to infinity. Therefore, we are naturally led to study singular Neumann problems for stationary Hamilton-Jacobi equations. We establish the existence, stability and comparison results for singular Neumann problems and apply the results for a large-time asymptotic profile on the effective domain of viscosity solutions of Hamilton-Jacobi equations with noncoercive Hamiltonian. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69778 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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