9 citations · 25 across the 11 of their papers we have counts for
11 papers
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…
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…
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…
A solution to the heat equation with a cubic moving boundary
Gerardo Hernandez-del-Valle
In this work we find a solution to problem of the heat equation which is annihiliated at a cubic boundary . The solution turns out to be the convolution between the fundamental…
On the zeros of the Pearcey integral and a Rayleigh-type equation
Gerardo Hernández-del-Valle
In this work we find a sequence of functions at which the Pearcey function is identically zero. The sequence of functions can be expressed in terms of a second order non-linear ODE…
On the first time that an Ito process hits a barrier
Gerardo Hernandez-del-Valle
This work deals with first hitting time densities of Ito processes whose local drift can be modeled in terms of a solution to Burgers equation. In particular, we derive the densiti…