On the elasto-plastic filtration equation

We study the fully nonlinear heat equation b(∂tu)∂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− ̸= b+ being two positive constants. This equation models the flow of an elastic fluid in an elasto-plastic porous medium. We a...

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Autores principales: de Pablo, Arturo, Quirós, Fernando, Rossi, Julio D.
Formato: info:eu-repo/semantics/preprint
Lenguaje:Inglés
Publicado: Arxiv 2025
Materias:
Física
Dinámica de Fluidos
Phisics
Fluid Dynamics
Acceso en línea:https://repositorio.utdt.edu/handle/20.500.13098/13905
Aporte de:
Repositorio Digital Universidad Torcuato Di Tella de Universidad Torcuato Di Tella
id I57-R163-20.500.13098-13905
record_format dspace
spelling I57-R163-20.500.13098-139052025-12-16T05:03:33Z On the elasto-plastic filtration equation de Pablo, Arturo Quirós, Fernando Rossi, Julio D. Física Dinámica de Fluidos Phisics Fluid Dynamics We study the fully nonlinear heat equation b(∂tu)∂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− ̸= 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 → ∞ and when b− → 0+ or b+ → +∞. We also characterize solutions of the problem as limits of a minimization dynamic game. Arxiv 2025-12-15T18:09:13Z 2025-12-10 info:eu-repo/semantics/preprint https://repositorio.utdt.edu/handle/20.500.13098/13905 eng Arxiv info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-sa/2.5/ar/ 26 p. application/pdf application/pdf
institution Universidad Torcuato Di Tella
institution_str I-57
repository_str R-163
collection Repositorio Digital Universidad Torcuato Di Tella
language Inglés
orig_language_str_mv eng
topic Física
Dinámica de Fluidos
Phisics
Fluid Dynamics
spellingShingle Física
Dinámica de Fluidos
Phisics
Fluid Dynamics
de Pablo, Arturo
Quirós, Fernando
Rossi, Julio D.
On the elasto-plastic filtration equation
topic_facet Física
Dinámica de Fluidos
Phisics
Fluid Dynamics
description We study the fully nonlinear heat equation b(∂tu)∂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− ̸= 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 → ∞ and when b− → 0+ or b+ → +∞. We also characterize solutions of the problem as limits of a minimization dynamic game.
format info:eu-repo/semantics/preprint
author de Pablo, Arturo
Quirós, Fernando
Rossi, Julio D.
author_facet de Pablo, Arturo
Quirós, Fernando
Rossi, Julio D.
author_sort de Pablo, Arturo
title On the elasto-plastic filtration equation
title_short On the elasto-plastic filtration equation
title_full On the elasto-plastic filtration equation
title_fullStr On the elasto-plastic filtration equation
title_full_unstemmed On the elasto-plastic filtration equation
title_sort on the elasto-plastic filtration equation
publisher Arxiv
publishDate 2025
url https://repositorio.utdt.edu/handle/20.500.13098/13905
work_keys_str_mv AT depabloarturo ontheelastoplasticfiltrationequation
AT quirosfernando ontheelastoplasticfiltrationequation
AT rossijuliod ontheelastoplasticfiltrationequation
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