Uniqueness in a class of Hamilton-Jacobi equations with constraints. (Unicité pour une classe d’équations de Hamilton-Jacobi avec contraintes.) (English. Abridged French version) Zbl 1343.35064
Summary: In this note, we discuss a class of time-dependent Hamilton-Jacobi equations depending on a function of time, this function being chosen in order to keep the maximum of the solution of the constant value 0. The main result of the note is that the full problem has a unique classical solution. The motivation is a selection-mutation model that, in the limit of small diffusion, exhibits concentration on the zero-level set of the solution to the Hamilton-Jacobi equation. The uniqueness result that we prove implies strong convergence and error estimates for the selection-mutation model.
MSC:
| 35F21 | Hamilton-Jacobi equations |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 35F25 | Initial value problems for nonlinear first-order PDEs |
| 70H20 | Hamilton-Jacobi equations in mechanics |
References:
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