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Hokkaido University Preprint Series in Mathematics >
Hamilton-Jacobi equations with discontinuous source terms
| Title: | Hamilton-Jacobi equations with discontinuous source terms |
| Authors: | GIGA, YOSHIKAZU Browse this author | | HAMAMUKI, NAO Browse this author |
| Keywords: | viscosity solutions | | Hamilton-Jacobi equations | | discontinuous Hamiltonians |
| Issue Date: | 24-Oct-2011 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 987 |
| Start Page: | 1 |
| End Page: | 38 |
| Abstract: | We study the initial-value problem for a Hamilton-Jacobi equation whose Hamiltonian is dis- continuous with respect to state variables. Our motivation comes from a model describing the two dimensional nucleation in crystal growth phenomena. A typical equation has a semicontinu- ous source term. We introduce a new notion of viscosity solutions and prove among other results that the initial-value problem admits a unique global-in-time uniformly continuous solution for any bounded uniformly continuous initial data. We also give a representation formula of the solution as a value function by the optimal control theory with a semicontinuous running cost function. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69793 |
| 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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