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On cell problems for Hamilton-Jacobi equations with non-coercive Hamiltonians and its application to homogenization problems
| Title: | On cell problems for Hamilton-Jacobi equations with non-coercive Hamiltonians and its application to homogenization problems |
| Authors: | HAMAMUKI, NAO Browse this author | | Nakayasu, Atsushi Browse this author | | Namba, Tokinaga Browse this author |
| Keywords: | Cell Problem | | Homogenization | | Hamilton-Jacobi Equation | | Non-coercive Hamiltonian | | Viscosity Solution | | Faceted Crystal Growth | | Generalized Effective Hamiltonian | | Solvability Set |
| Issue Date: | 6-Apr-2015 |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1070 |
| Start Page: | 1 |
| End Page: | 24 |
| Abstract: | We study a cell problem arising in homogenization for a Hamilton-Jacobi equation whose Hamiltonian is not coercive. We introduce a generalized notion of effective Hamiltonians by approximating the equation and characterize the solvability of the cell problem in terms of the generalized effective Hamiltonian. Under some sufficient conditions, the result is applied to the associated homogenization problem. We also show that homogenization for non-coercive equations fails in general. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69874 |
| 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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