An exact viscosity solution to a Hamilton–Jacobi–Bellman quasi-variational inequality for animal population management.

Yaegashi, Yuta; Yoshioka, Hidekazu; Tsugihashi, Kentaro; Fujihara, Masayuki

We formulate a stochastic impulse control model for animal population management and a candidate of exact solutions to a Hamilton–Jacobi–Bellman quasi-variational inequality. This model has a qualitatively different functional form of the performance index from the existing monotone ones. So far, optimality and unique solvability of the Hamilton–Jacobi–Bellman quasi-variational inequality has not been investigated, which are thus addressed in this paper. We present a candidate of exact solutions to the Hamilton–Jacobi–Bellman quasi-variational inequality and prove its optimality and unique solvability within a certain class of solutions in a viscosity sense. We also present and examine a dynamical system-based numerical method for computing coefficients in the exact solutions.

WILDLIFE management; VISCOSITY solutions; DYNAMICAL systems; MATHEMATICAL equivalence

Journal of Mathematics in Industry, 2019, Vol 9, Issue 1, pN.PAG

2190-5983

Academic Journal

10.1186/s13362-019-0062-y