2022-05-19T06:45:59Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/697802018-04-25T23:44:11Zhdl_2115_45007hdl_2115_116Large-time Asymptotics for One-dimensional DirichletProblems for Hamilton-Jacobi Equations withNoncoercive HamiltoniansYoshikazu, GigaQing, LiuHiroyoshi, MitakeLarge-time BehaviorBoundary Value ProblemsNoncoercive Hamilton-Jacobi EquationsViscosity Solution410We study large-time asymptotics for a class of noncoercive Hamilton-Jacobi equations with Dirichlet boundary condition in one space dimension. We prove that the average growth rate of a solution is constant only in a subset of the whole domain and give the asymptotic pro¯le in the subset. We show that the large-time behavior for noncoercive problems may depend on the space variable in general, which is di®erent from the usual results under the coercivity condition. This work is an extension with more rigorous analysis of a recent paper by E. Yokoyama, Y. Giga and P. Rybka, in which a growing crystal model is established and the asymptotic behavior described above is first discovered.Departmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69780info:doi/10.14943/84120https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69780/1/pre973.pdfHokkaido University Preprint Series in Mathematics9732302011-01-20engpublisher