Abstract
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.
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