Infinity of solutions to initial-boundary value problems for linear constant-coefficient evolution PDEs on semi-infinite intervals
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914179756064768 |
|---|---|
| author | Chatziafratis, Andreas Kamvissis, Spyridon |
| author_facet | Chatziafratis, Andreas Kamvissis, Spyridon |
| contents | In this short communication, we announce an algorithmic procedure for constructing non-uniqueness counter-examples of classical solutions to initial-boundary-value problems for a wide class of linear evolution partial differential equations, of any order and with constant coefficients, formulated in a quarter-plane. Our approach relies on analysis of regularity and asymptotic properties, near the boundary of the spatio-temporal domain, of closed-form integral-representation formulae derived via complex-analytic techniques and rigorous implementation of the modern PDE technique known as Fokas unified transform method. In order to elucidate the novel idea and demonstrate the proposed technique in a self-contained fashion, we explicitly present its application to two concrete examples, namely the heat equation and the linear KdV equation with Dirichlet data. New uniqueness theorems for these two models are also presented herein. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04670 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinity of solutions to initial-boundary value problems for linear constant-coefficient evolution PDEs on semi-infinite intervals Chatziafratis, Andreas Kamvissis, Spyridon Analysis of PDEs Mathematical Physics Complex Variables In this short communication, we announce an algorithmic procedure for constructing non-uniqueness counter-examples of classical solutions to initial-boundary-value problems for a wide class of linear evolution partial differential equations, of any order and with constant coefficients, formulated in a quarter-plane. Our approach relies on analysis of regularity and asymptotic properties, near the boundary of the spatio-temporal domain, of closed-form integral-representation formulae derived via complex-analytic techniques and rigorous implementation of the modern PDE technique known as Fokas unified transform method. In order to elucidate the novel idea and demonstrate the proposed technique in a self-contained fashion, we explicitly present its application to two concrete examples, namely the heat equation and the linear KdV equation with Dirichlet data. New uniqueness theorems for these two models are also presented herein. |
| title | Infinity of solutions to initial-boundary value problems for linear constant-coefficient evolution PDEs on semi-infinite intervals |
| topic | Analysis of PDEs Mathematical Physics Complex Variables |
| url | https://arxiv.org/abs/2512.04670 |