Viscosity Solutions of Cauchy Problems for Hamilton-Jacobi Equations
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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.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.
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- 湘南工科大学紀要 = Memoirs of Shonan Institute of Technology
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湘南工科大学紀要 = Memoirs of Shonan Institute of Technology 28 (1), 101-105, 1994-03-25
湘南工科大学
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詳細情報
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- CRID
- 1571980077605462528
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- NII論文ID
- 120005538952
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- NII書誌ID
- AN10400308
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- ISSN
- 09192549
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- Web Site
- http://id.nii.ac.jp/1266/00000298/
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- 本文言語コード
- ja
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- データソース種別
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