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

Journal of Mathematics in Industry

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[1] 0000 0000 8661 1590, grid.411621.1, Graduate School of Natural Science and Technology, Shimane University, Matsue City, Japan;0000 0004 0372 2033, grid.258799.8, Graduate School of Agriculture, Kyoto University, Kyoto City, Japan;0000 0004 0372 2033, grid.258799.8, Graduate School of Agriculture, Kyoto University, Kyoto City, Japan;0000 0004 0614 710X, grid.54432.34, Research Fellow of Japan Society for the Promotion of Science, Tokyo, Japan;

关键词: Population management;    Threshold control;    Hamilton–Jacobi–Bellman quasi-variational inequalities;    Viscosity solution;    Feeding damage;    Uniqueness and existence of solution;    Optimality of control;   

DOI  :  10.1186/s13362-019-0062-y

来源: publisher

【 摘 要 】

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.

【 授权许可】

CC BY