Uniqueness in a class of Hamilton-Jacobi equations with constraints

2015/02/13 by Sepideh Mirrahimi, Jean‐Michel Roquejoffre, Mirrahimi, Sepideh +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Analysis of PDEs (math.AP) #Evolution and Genetic Dynamics #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models

paper · doi:10.48550/arxiv.1502.04002

openalex publication_date 2015/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 to 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 which, in the limit of small diffusion, exhibits concentration on the zero level set of the solution of 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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