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Elliptic systems generating a positive semigroup are decoupled

Year: 2025

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2509.19055

Authors: Arendt, Wolfgang, ter Elst, A. F. M., Sauter, Manfred

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4416254408

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