Constructive solutions of the heat equation with Stieltjes derivatives
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916023180984320 |
|---|---|
| author | Senín, Clara Tojo, F. Adrián F. |
| author_facet | Senín, Clara Tojo, F. Adrián F. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18585 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Constructive solutions of the heat equation with Stieltjes derivatives Senín, Clara Tojo, F. Adrián F. Analysis of PDEs 26A24, 35K20, 35K05 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. |
| title | Constructive solutions of the heat equation with Stieltjes derivatives |
| topic | Analysis of PDEs 26A24, 35K20, 35K05 |
| url | https://arxiv.org/abs/2605.18585 |