Unique continuation for a reaction-diffusion system with cross diffusion
Bin Wu, Ying Gao, Zewen Wang, Qun Chen · Journal of Inverse and Ill-Posed Problems · 2019
Abstract This paper concerns unique continuation for a reaction-diffusion system with cross diffusion, which is a drug war reaction-diffusion system describing a simple dynamic model of a drug epidemic in an idealized community. We first establish a Carleman estimate for this strongly coupled reaction-diffusion system. Then we apply the Carleman estimate to prove the unique continuation, which means that the Cauchy data on any lateral boundary determine the solution uniquely in the whole domain.