2023-03-24T16:14:44Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/697932022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Hamilton-Jacobi equations with discontinuous source termsGIGA, YOSHIKAZUHAMAMUKI, NAOopen accessviscosity solutionsHamilton-Jacobi equationsdiscontinuous Hamiltonians410We 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.Department of Mathematics, Hokkaido University2011-10-24engdepartmental bulletin paperVoRhttps://doi.org/10.14943/84134http://hdl.handle.net/2115/6979310.14943/84134Hokkaido University Preprint Series in Mathematics987138https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69793/1/pre987.pdfapplication/pdf1.96 MB2011-10-24