1. Sparse source identification of linear diffusion–advection equations by adjoint methods
- Author
-
Azahar Monge and Enrique Zuazua
- Subjects
0209 industrial biotechnology ,General Computer Science ,Advection ,Mechanical Engineering ,020208 electrical & electronic engineering ,Mass diffusivity ,Time horizon ,02 engineering and technology ,Linear diffusion ,Identification (information) ,symbols.namesake ,020901 industrial engineering & automation ,Control and Systems Engineering ,Kronecker delta ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,Applied mathematics ,Electrical and Electronic Engineering ,State distribution ,Mathematics - Abstract
We present an algorithm for the time-inversion of diffusion–advection equations, based on the adjoint methodology. Given a final state distribution our main aim is to recover sparse initial conditions, constituted by a finite combination of Kronecker deltas, identifying their location and mass. We discuss the strengths of the adjoint machinery and the difficulties that are to be faced, in particular when the diffusivity coefficient or the time horizon is large.
- Full Text
- View/download PDF