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Hamilton-Jacobi equations with discontinuous source terms

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84134

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
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

Submitter: 数学紀要登録作業用

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