2025/05/23 by Yiqun Li, Mengmeng Liu, Li, Yiqun +4
Mathematics · #math.OC
paper · pdf · doi:10.48550/arxiv.2505.17678
This work investigates the optimal control of the variable-exponent subdiffusion, which extends the work [Gunzburger and Wang, SIAM J. Control Optim. 2019] to the variable-exponent case to account for the multiscale and crossover diffusion behavior. To resolve the difficulties caused by the leading variable-exponent operator, we adopt the convolution method to reformulate the model into an equivalent but more tractable form, and then prove the well-posedness and weighted regularity of the optimal control. As the convolution kernels in reformulated models are indefinite-sign, non-positive-definite, and non-monotonic, we adopt the discrete convolution kernel approach in numerical analysis to show the O(τ(1+|lnτ|)+h2) accuracy of the schemes for state and adjoint equations. Numerical experiments are performed to substantiate the theoretical findings.