Inverse Problem: Simultaneous Reconstruction of Multiple Coefficients in Tridiagonal Competitive Reaction-Diffusion Systems with Positive Feedback

Abstract

This paper establishes uniqueness results for solving inverse problems involving multiple non-constant coefficients in a trio of parabolic equations modeling tridiagonal competitive diffusion. We demonstrate that six coefficients in the system-namely, the reaction coefficients r₁, r₂, r₃ and the interaction coefficients a₁₁, a₂₂, a₃₃-can be uniquely determined under the following conditions: 1. The coefficients belong to the Cⁿ ([a, b]) function space. 2. Pointwisemeasurements of the solution components (u₁, u₂, u₃) along with their spatial derivatives and are available at a single spatial point x₀. Notably, these measurements only need to be observed over an arbitrarily small time interval (0, ε).