Author

P. Zegeling

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Preprint Sep 2026

Well-posedness and Blow-up in a semilinear heat equation with variable-order Scarpi memory

We study the semilinear heat equation ${}^{S}D_0^{\alpha(t)}u=\Delta u+u^p$ on $\RR^n$, where $p>1$ and the Scarpi order changes exponentially from $\alpha_1$ to $\alpha_2$, with $0<\alpha_1,\alpha_2<1$. We establish local and maximal mild well-posedness for abstract Scarpi--Volterra equations. For the whole-space heat...

Yu-Shuang Pu, P. Zegeling · 0 citations

Preprint Oct 2026

Convolution Quadrature with Adaptive History Compression for Variable-Order Fractional Reaction--Diffusion Equations

We develop a fully implicit fast method for semilinear variable-order fractional reaction--diffusion equations with periodic fractional diffusion and exponential-transition Scarpi memory. A Volterra-resolvent analysis establishes local well-posedness and temporal regularity estimates that describe the weak initial sing...

Yu-Shuang Pu, P. Zegeling · 0 citations