From the 2 of 7 linked papers with an AI index.
7 papers
Stable Reduction of Unresolved Dynamics: An Operator-Theoretic Framework
Hiroki Ishizaka
Dimension reduction removes variables, but a reliable reduction should not erase their dynamical influence. We study this principle for linear block evolution systems on resolved a…
Graph-space well-posedness for diffusion equations with degenerate instantaneous diffusion
Hiroki Ishizaka
The paper establishes well‑posedness and stability for diffusion equations with completely monotone memory when the instantaneous diffusion term is only non‑negative, using an exte…
Coercivity structure of positive-type memory: exact gaps, critical horizons, and singular limits
Hiroki Ishizaka
The paper examines diffusion equations with positive‑type (completely monotone) memory in regimes where the instantaneous diffusion loses coercivity, proving that such memory canno…
Low-order CR--RT equilibrated-flux certification for semilinear problems on anisotropic meshes
Hiroki Ishizaka
We develop a low-order Crouzeix--Raviart--Raviart--Thomas (CR--RT) equilibrated-flux certification workflow for finite element approximations of semilinear diffusion--reaction prob…
Weighted well-posedness and kernel stability for coercive evolution equations with measure-valued delays
Hiroki Ishizaka
We consider coercive evolution equations with measure-valued delay on a Gelfand triple. The delayed feedback is induced by a bounded form on and may contain principal spatial d…
Nitsche's method under a semi-regular mesh condition
Hiroki Ishizaka
Nitsche's method is a numerical approach that weakly enforces boundary conditions for partial differential equations. In recent years, Nitsche's method has experienced a revival ow…