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arXiv · 2509.19055

Elliptic systems generating a positive semigroup are decoupled

Wolfgang Arendt·A. F. M. ter Elst·Manfred Sauter
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Abstract

We show that the semigroup associated to a second-order elliptic system is positive if and only if the differential equations are essentially decoupled and the coefficients are real-valued. This means the system can be replaced by an equivalent decoupled system (which defines the same semigroup). Instead of matrix coefficients we more generally consider operator-valued coefficients, which leads to interesting additional difficulties with respect to Banach space valued integration.

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Wolfgang Arendt, A. F. M. ter Elst, Manfred Sauter. 2025-09-23. Elliptic systems generating a positive semigroup are decoupled. https://arxiv.org/abs/2509.19055

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