Geodesic
On the uniqueness of solutions to one-dimensional constrained Hamilton-Jacobi equations
Minimax theory and its applications, Tome 6 (2021) no. 1
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The goal of this paper is to study the uniqueness of solutions to a constrained Hamilton-Jacobi equation{ut = u2x + R(x, I(t)) in R × (0, ∞),maxR u(·, t) = 0 on [0, ∞),with an initial condition u(x, 0) = u0(x) on R. A reaction term R(x, I(t)) is given while I(t) is an unknown constraint (Lagrange multiplier) that forces maximum of u to be always zero. In the paper, we prove uniqueness of a pair of unknowns (u, I) using dynamic programming principle for a particular class of non-separable reaction R(x, I(t)) when the space is one-dimensional.
Mots-clés : Hamilton-Jacobi equation with constraint, selection-mutation model 
@article{MTA_2021_6_1_a4,
     author = {Yeoneung Kim},
     title = {On the uniqueness of solutions to one-dimensional constrained {Hamilton-Jacobi} equations},
     journal = {Minimax theory and its applications},
     year = {2021},
     volume = {6},
     number = {1},
     zbl = {1466.35003},
     url = {http://geodesic.mathdoc.fr/item/MTA_2021_6_1_a4/}
}
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Yeoneung Kim. On the uniqueness of solutions to one-dimensional constrained Hamilton-Jacobi equations. Minimax theory and its applications, Tome 6 (2021) no. 1. http://geodesic.mathdoc.fr/item/MTA_2021_6_1_a4/