4 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
We study diffusion equations with completely monotone memory when the instantaneous diffusion form is merely non-negative and may therefore lose coercivity. For a kernel whose Bern…
Coercivity structure of positive-type memory: exact gaps, critical horizons, and singular limits
Hiroki Ishizaka
We study diffusion equations with positive-type memory in the degenerate regime where the instantaneous diffusion may lose coercivity. The basic question is simple: can a completel…
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…