On the elasto-plastic filtration equation
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915664952819712 |
|---|---|
| author | de Pablo, Arturo Quiros, Fernando Rossi, Julio D. |
| author_facet | de Pablo, Arturo Quiros, Fernando Rossi, Julio D. |
| contents | We study the fully nonlinear heat equation $b(\partial_tu)\partial_tu=Δu$ posed in a bounded domain with Dirichlet boundary conditions. Here $b(s)=b^-$ if $s<0$, $b(s)=b^+$ if $s>0$, $b^-\neq b^+$ being two positive constants. This equation models the flow of an elastic fluid in an elasto-plastic porous medium. We are interested in the existence and uniqueness of viscosity solutions and in their asymptotic behaviour as $t\to\infty$ and when $b^-\to 0^+$ or $b^+\to +\infty$. We also characterize solutions of the problem as limits of a minimization dynamic game. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09298 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the elasto-plastic filtration equation de Pablo, Arturo Quiros, Fernando Rossi, Julio D. Analysis of PDEs 35K55, 35B30, 35B40, 35Q91, 35D40 We study the fully nonlinear heat equation $b(\partial_tu)\partial_tu=Δu$ posed in a bounded domain with Dirichlet boundary conditions. Here $b(s)=b^-$ if $s<0$, $b(s)=b^+$ if $s>0$, $b^-\neq b^+$ being two positive constants. This equation models the flow of an elastic fluid in an elasto-plastic porous medium. We are interested in the existence and uniqueness of viscosity solutions and in their asymptotic behaviour as $t\to\infty$ and when $b^-\to 0^+$ or $b^+\to +\infty$. We also characterize solutions of the problem as limits of a minimization dynamic game. |
| title | On the elasto-plastic filtration equation |
| topic | Analysis of PDEs 35K55, 35B30, 35B40, 35Q91, 35D40 |
| url | https://arxiv.org/abs/2512.09298 |