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math.AP2026
Stationary Grading and Heat-Transported Moving Boundaries: From the Cubic Case to Two Fourth-Order Branches
Gerardo Hernández-del-Valle
We study zeros transported by the heat semigroup from stationary solutions of the sparse operators $L_n=c_{n,0}\D^n+c_{0,n-1}x^{n-1}$. The starting point is the exact cubic boundar…
math.AP2026
Heat--Airy Transport of Differential Operators and Moving Boundaries
Gerardo Hernández-del-Valle
We study the transport of polynomial differential operators under the two-parameter commuting evolution \[ P_{t,s} = \exp\left( \frac{t}{2}D^2-\frac{s}{3}D^3 \right), \qquad D=\fra…
math.AP2026
A Recursive Representation of Compatibility Matrices for Transported Differential Operators
Gerardo Hernandez-del-Valle
We develop a recursive algebraic framework for the compatibility matrices arising in moving-boundary problems for the heat equation. Such matrices naturally appear in the analysis…