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Operator splitting for nonlinear reaction-diffusion systems with an entropic structure: Singular perturbation and order reduction. (English) Zbl 1060.65105
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.

##### MSC:
 65M20 Method of lines for initial value and initial-boundary value problems involving PDEs 35B25 Singular perturbations in context of PDEs 35K57 Reaction-diffusion equations
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