Shape preservation of evolution equations

Feb 04, 2026

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This work discusses the nature of shape preservation in evolution equations, highlighting key concepts such as positivity, monotonicity, and convexity preservation. Various examples illustrate these preservation traits in the context of mathematical modeling. Special attention is given to Wentzell boundary conditions and negative convexity. Theoretical underpinnings are supported by the Miyadera-Voigt perturbation and its generalization of the Arendt-Rhandi theorem. The paper aims to contribute to the understanding of shape preservation in the dynamics of nonlocal Wentzell boundary conditions.

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Shape preservation of evolution equations

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Shape preservationofevolutionequations András Bátkai, ELTE Budapest A. Bobrowski (Lublin) TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA
Whatisshape? Whatisshapepreservation? Examples: Positivitypreservation: Monotonicitypreservation: Convexity/concavitypreservation: More involved:

Monotonicity: Convexity: Wentzellboundaryconditions Negative Convexity: Convexity:
Somemorereferences: convexitypreservationofgeneralnonlocalWentzellb.c.
Theorem:
Theorem: (Miyadera-Voigt perturbation) (generalizationof Arendt-Rhandi)
Delay-equations Reference: SemigroupsforDelayEquations (withS. Piazzera) A K Peters, 2005
TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA