Boundary Control of Chemotaxis Reaction Diffusion System

Necessary Conditions for Optimal Boundary Control Problem Governed by Some Chemotaxis Equations

“…By using Lemma 3.1, we obtain the existence of the optimal control U ∈ (H 1 (0, S)) 2 . The proof is similar to that of [7].…”

“…In this section, we recall the existence and uniqueness of a local solution for (1.1)( [5,7]). To derive the existence of solutions for (1.1), we reduce (1.1) to a homogeneous problem.…”

“…We refer to [2,3,5,6] and the references for (1.1). Many papers have already been published to study the optimal control problems for nonlinear parabolic equations(see [1,3,6,7]). In [7], Ryu studied the existence of the optimal boundary control for the chemotaxis diffusion equations when the boundary control is given in the space H 2 (0, T ).…”

“…Many papers have already been published to study the optimal control problems for nonlinear parabolic equations(see [1,3,6,7]). In [7], Ryu studied the existence of the optimal boundary control for the chemotaxis diffusion equations when the boundary control is given in the space H 2 (0, T ). However, in this paper we obtain the existence and the necessary conditions of the optimal boundary control in the space (H 1 (0, T )) 2 .…”

An efficient and robust numerical algorithm for estimating parameters in Turing systems

“…When a cost functional measuring the discrepancy between solutions and target functions is formulated, constrained optimization techniques are employed (one-shot, sensitivity or adjoint-based methods) to construct an iterative algorithm [10,29] for estimating model parameters. There are numerous works in the literature that apply optimal control theory to reaction-diffusion systems [4][5][6]8,12,13,16,19,20,45]. However, relatively few works focus on estimating parameters in nonlinear reaction-diffusion systems [1,14,24,28], and to the best of our knowledge, none address parameter estimation for the Turing reaction-diffusion model.…”