Operator splitting for nonlinear reaction-diffusion systems with an entropic structure: Singular perturbation and order reduction
The authors are interested in reaction-diffusion problems of the type \((U^\varepsilon \in\mathbb{R}^n)\): \[ \partial_tU^\varepsilon_x \cdot\bigl(B (U^\varepsilon) \partial_xU^\varepsilon\bigr)=F^\varepsilon,\quad x\in \mathbb{R}^d,\;t\geq 0 \] where \(B(U^\varepsilon)\), called diffusion matrix, is a tensor of order \(d\times d\times n\). The solution of this dynamical system is denoted by \(U^\varepsilon=T^t_\varepsilon U_0\), where \(U_0\) is the initial condition and \(\varepsilon>0\) is a small parameter. Then the singular perturbation results are presented followed by various operator splittings. The theoretical results are illustrated numerically together with the influence of the discretization on the results.
scientific article; zbMATH DE number 2121822