2023/02/20 by Alberto Bressan, Bressan, Alberto, Minyan Zhang +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #35C07 #49J15 #49J20 #49K15 #Analysis of PDEs (math.AP) #Evolution and Genetic Dynamics #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2302.09728
openalex publication_date 2023/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a family of controlled reaction-diffusion equations, describing the spatial spreading of an invasive biological species. For a given propagation speed c∈I R, we seek a control with minimum cost, which achieves a traveling profile with speed c. For various nonlinear models, the existence of a (possibly measure valued) optimal control is proved, together with necessary conditions for optimality. In the last section we study a case where the wave speed cannot be modified by any control with finite cost. The present analysis is motivated by the recent results in arXiv:2201.01723 and arXiv:2108.09321, showing how a control problem for a reaction-diffusion equation can be approximated by a simpler problem of optimal control of a moving set.