Hamilton-Jacobi Equations with Discontinuous Source Terms |
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Authors: | Yoshikazu Giga |
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Affiliation: | Graduate School of Mathematical Sciences , University of Tokyo , Tokyo , Japan |
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Abstract: | We study the initial-value problem for a Hamilton-Jacobi equation whose Hamiltonian is discontinuous 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 semicontinuous 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. |
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Keywords: | Discontinuous Hamiltonians Hamilton-Jacobi equations Viscosity solutions |
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