Hamilton-Jacobi equations with discontinuous source terms

GIGA, YOSHIKAZU; HAMAMUKI, NAO

Hokkaido University Preprint Series in Mathematics, 2011, 987, 1-38

Permalink : https://doi.org/10.14943/84134

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アクセス権	open access
DOI	https://doi.org/10.14943/84134
URI	https://hdl.handle.net/2115/69793
タイトル	Hamilton-Jacobi equations with discontinuous source terms
著者	著者名 GIGA, YOSHIKAZU
著者	著者名 HAMAMUKI, NAO
言語	英語
キーワード	viscosity solutions
	Hamilton-Jacobi equations
	discontinuous Hamiltonians
発行日	2011-10-24
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	987
ページ	1-38
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record