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arXiv · 2504.18295

Sharp decay estimates and numerical analysis for weakly coupled systems of two subdiffusion equations

Zhiyuan Li·Yikan Liu·Kazuma Wada
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Abstract

This paper investigates the initial-boundary value problem for weakly coupled systems of time-fractional subdiffusion equations with spatially and temporally varying coupling coefficients. By combining the energy method with the coercivity of fractional derivatives, we convert the original partial differential equations into a coupled ordinary differential system. Through Laplace transform and maximum principle arguments, we reveal a dichotomy in decay behavior: When the highest fractional order is less than one, solutions exhibit sublinear decay, whereas systems with the highest order equal to one demonstrate a distinct superlinear decay pattern. This phenomenon fundamentally distinguishes coupled systems from single fractional diffusion equations, where such accelerated superlinear decay never occurs. Numerical experiments employing finite difference methods and implicit discretization schemes validate the theoretical findings.

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Zhiyuan Li, Yikan Liu, Kazuma Wada. 2025-10-15. Sharp decay estimates and numerical analysis for weakly coupled systems of two subdiffusion equations. https://doi.org/10.1016/j.jde.2025.113826

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