2023-03-30T23:12:53Zhttps://shonan-it.repo.nii.ac.jp/?action=repository_oaipmhoai:shonan-it.repo.nii.ac.jp:000003062015-01-29T05:45:26Z00002:00021
Viscosity Solutions of Cauchy Problems for Hamilton-Jacobi EquationsViscosity Solutions of Cauchy Problems for Hamilton-Jacobi Equationsjpnhttp://id.nii.ac.jp/1266/00000298/Departmental Bulletin PaperKobayashi, KazuoThe viscosity solutions of the Cauchy problem u_t+H(x, u, Du)=0,u(x, 0)=u_0(x) in R^N, where H : R_N×R×R^N→R is a continuous function, are considered. We prove an existence and uniqueness theorem under a condition which is more general than the usual one with respect to the u dependence of the Hamiltonian H(x, u, p). This generalized condition would not necessarily guarantee that the stationary problem u+H(x, u, Du)=ƒ in R^N has a continuous viscosity solution. Our main method is based on the technique from nonlinear semigroup theory.The viscosity solutions of the Cauchy problem u_t+H(x, u, Du)=0,u(x, 0)=u_0(x) in R^N, where H : R_N×R×R^N→R is a continuous function, are considered. We prove an existence and uniqueness theorem under a condition which is more general than the usual one with respect to the u dependence of the Hamiltonian H(x, u, p). This generalized condition would not necessarily guarantee that the stationary problem u+H(x, u, Du)=ƒ in R^N has a continuous viscosity solution. Our main method is based on the technique from nonlinear semigroup theory.湘南工科大学紀要 = Memoirs of Shonan Institute of Technology2811011051994-03-25湘南工科大学09192549AN10400308https://shonan-it.repo.nii.ac.jp/?action=repository_action_common_download&item_id=306&item_no=1&attribute_id=22&file_no=12014-11-25