Existence and stability of the Riemann solutions for a non-symmetric Keyfitz--Kranzer type model
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908529785307136 |
|---|---|
| author | Barthwal, Rahul Rohde, Christian Sen, Anupam |
| author_facet | Barthwal, Rahul Rohde, Christian Sen, Anupam |
| contents | In this article, we develop a new hyperbolic model governing the first-order dynamics of a thin film flow under the influence of gravity and solute transport. The obtained system turns out to be a non-symmetric Keyfitz-Kranzer type system. We find an entire class of convex entropies in the regions where the system remains strictly hyperbolic. By including delta shocks, we prove the existence of unique solutions of the Riemann problem. We analyze their stability with respect to the perturbation of the initial data and to the gravity and surface tension parameters. Moreover, we discuss the large time behaviour of the solutions of the perturbed Riemann problem and prove that the initial Riemann states govern it. Thus, we confirm the structural stability of the Riemann solutions under the perturbation of initial data. Finally, we validate our analytical results with well-established numerical schemes for this new system of conservation laws. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07391 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence and stability of the Riemann solutions for a non-symmetric Keyfitz--Kranzer type model Barthwal, Rahul Rohde, Christian Sen, Anupam Analysis of PDEs 35L40 35L45 35L65 76A20 In this article, we develop a new hyperbolic model governing the first-order dynamics of a thin film flow under the influence of gravity and solute transport. The obtained system turns out to be a non-symmetric Keyfitz-Kranzer type system. We find an entire class of convex entropies in the regions where the system remains strictly hyperbolic. By including delta shocks, we prove the existence of unique solutions of the Riemann problem. We analyze their stability with respect to the perturbation of the initial data and to the gravity and surface tension parameters. Moreover, we discuss the large time behaviour of the solutions of the perturbed Riemann problem and prove that the initial Riemann states govern it. Thus, we confirm the structural stability of the Riemann solutions under the perturbation of initial data. Finally, we validate our analytical results with well-established numerical schemes for this new system of conservation laws. |
| title | Existence and stability of the Riemann solutions for a non-symmetric Keyfitz--Kranzer type model |
| topic | Analysis of PDEs 35L40 35L45 35L65 76A20 |
| url | https://arxiv.org/abs/2509.07391 |