A uniqueness result for an inverse problem of the steady state convection-diffusion equation

TL;DR

This paper proves that the velocity field in a steady state convection-diffusion equation can be uniquely identified from boundary measurements if the velocity is sufficiently smooth, specifically H"older continuous with exponent greater than 2/3.

Contribution

It establishes a new uniqueness result for the inverse boundary value problem for the convection-diffusion equation with H"older continuous velocity fields.

Findings

Unique determination of velocity field from boundary data.

Validity for velocity fields with H"older continuity exponent > 2/3.

Advances understanding of inverse problems in convection-diffusion equations.

Abstract

We consider the inverse boundary value problem for the steady state convection diffusion equation. We prove that a velocity field $V$, is uniquely determined by the Dirichlet-to-Neumann map, when $V \in C^{0,\gamma} (\Omega)$, $2/3< \gamma \leq 1$, i.e. when $V$ is a H\"older continuous vector field with $2/3< \gamma \leq 1$.