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Shoji, H., Yokogawa, S., Iwamoto, R. and Yamada, K. (1990) Bifurcation Points of Periodic Triangular Patterns Obtained in Reaction-Diffusion System with Anisotropic Diffusion. Journal of Applied Mathematics and Physics, 10, 2341-2355.
https://doi.org/10.4236/jamp.2022.107159

has been cited by the following article:

• TITLE: Multi Parameter Adaptive Estimation of Reaction-Diffusion Equation

  AUTHORS: Shujing Wang

  KEYWORDS: Parameter Estimation, Adaptive Law, Backstepping Transformation

  JOURNAL NAME: Engineering, Vol.16 No.7, July 25, 2024

  ABSTRACT: This study addresses the problem of parameter estimation for a one-dimensional reaction-diffusion equation, involving both unknown domain parameters and unknown boundary parameters. The proposed approach utilizes the least-squares method to design an adaptive law for parameter estimation. The convergence analysis demonstrates that under persistent excitation conditions, the adaptive law converges exponentially to zero, indicating that the estimated parameters converge exponentially to their true values. Numerical simulations confirm the effectiveness. Furthermore, it is shown that within a certain range of the reaction coefficient, the auxiliary system acts as a state observer, providing an accurate estimate of the system state at an exponential rate.