Integral Equations and Operator Theory· 2026Q2
The Time-Periodic Cahn–Hilliard–Gurtin System on the Half Space as a Mixed-Order System with General Boundary Conditions
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- Q2SCImago
- 2026year
Short summary
A novel class of complementing boundary conditions is introduced and proven for the time-periodic Cahn-Hilliard-Gurtin system on a half space, extending Lopatinskiĭ–Shapiro conditions to time-periodic mixed-order systems.
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Key points
- Proved well-posedness and maximal regularity for the time-periodic Cahn-Hilliard-Gurtin system on a half space.
- Introduced a novel class of complementing boundary conditions.
- Extended Lopatinskiĭ–Shapiro conditions to time-periodic mixed-order systems with general boundary conditions.
- Showed that classical Lopatinskiĭ–Shapiro conditions are generally insufficient for mixed-order systems.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract A well-posedness and maximal regularity result for the time-periodic Cahn–Hilliard–Gurtin system in the half space is proved. For this purpose, we introduce a novel class of complementing boundary conditions, extending the classical Lopatinskiĭ–Shapiro conditions from elliptic and parabolic theory to time-periodic mixed-order systems with general boundary conditions. Moreover, we show that the classical Lopatinskiĭ–Shapiro conditions are in general insufficient for well-posedness of mixed-order systems.
The authors' abstract, as published at the source. Integral Equations and Operator Theory, 2026 · DOI ↗
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Field: Applied Mathematics
Applied MathematicsMathematics