Constructive solutions of the heat equation with Stieltjes derivatives
Analysis of PDEs
2026-05-19 v1
Abstract
In this work, we investigate the one-dimensional heat equation within the framework of Stieltjes calculus. We first consider the equation associated with two fixed derivators and develop a constructive approach to establish the existence of solutions. We then study the corresponding initial value problem and incorporate several types of boundary conditions. Finally, we introduce a notion of multivariable derivator, suitable for higher-dimensional settings, and obtain explicit solutions of the heat equation for relevant classes of such derivators.
Keywords
Cite
@article{arxiv.2605.18585,
title = {Constructive solutions of the heat equation with Stieltjes derivatives},
author = {Clara Senín and F. Adrián F. Tojo},
journal= {arXiv preprint arXiv:2605.18585},
year = {2026}
}