English
Related papers

Related papers: Well-posedness for a moving boundary model of an e…

200 papers

The analysis and homogenization of a moving boundary problem for a highly heterogeneous, periodic two-phase medium is considered. In this context, the normal velocity governing the motion of the interface separating the two competing phases…

Analysis of PDEs · Mathematics 2019-01-09 Michael Eden

We consider the Euler system set on a bounded convex planar domain, endowed with impermeability boundary conditions. This system is a model for the barotropic mode of the Primitive Equations on a rectangular domain. We show the existence of…

Analysis of PDEs · Mathematics 2013-08-19 Claude Bardos , Francesco Di Plinio , Roger Temam

We address semigroup well-posedness of the fluid-structure interaction of a linearized compressible, viscous fluid and an elastic plate (in the absence of rotational inertia). Unlike existing work in the literature, we linearize the…

Analysis of PDEs · Mathematics 2017-06-09 George Avalos , Pelin G. Geredeli , Justin T. Webster

Two phase solid-fluid mixture models are ubiquitous in biological applications. For instance, models for growth of tissues and biofilms combine time dependent and quasi-stationary boundary value problems set in domains whose boundary moves…

Analysis of PDEs · Mathematics 2024-01-17 Ana Carpio , Gema Duro

This dissertation resolves a longstanding discussion of a mathematical problem important in contaminant hydrogeology and chemical-reaction engineering, the proper mathematical description for a miscible solute undergoing longitudinal…

Analysis of PDEs · Mathematics 2007-05-23 W. J. Golz

In this paper we develop a model to describe the diffusion process in a porous medium. For the observed decrease in current yield, we propose other causes than difference in diffusivity, which we consider unaltered by the porous medium. The…

Chemical Physics · Physics 2012-05-10 P. C. T. DÁjello , G. L. Nunes , J. J. Piacentini , L. Lauck

We analyse dissipative boundary conditions for nonlinear hyperbolic systems in one space dimension. We show that a previous known sufficient condition for exponential stability with respect to the C^1-norm is optimal. In particular a known…

Analysis of PDEs · Mathematics 2014-03-10 Jean-Michel Coron , Hoai-Minh Nguyen

Initial-boundary value problem for linearized equations of motion of viscous barotropic fluid in a bounded domain is considered. Existence, uniqueness and estimates of weak solutions to this problem are derived. Convergence of the solutions…

Analysis of PDEs · Mathematics 2015-05-20 Nikolay Gusev

We deal with the obstacle problem for the porous medium equation in the slow diffusion regime $m>1$. Our main interest is to treat fairly irregular obstacles assuming only boundedness and lower semicontinuity. In particular, the considered…

Analysis of PDEs · Mathematics 2018-07-23 Riikka Korte , Pekka Lehtelä , Stefan Sturm

We consider the free boundary incompressible porous media equation which describes the dynamics of a density transported by a Darcy flow in the field of gravity, with a free boundary between the fluid region and the dry region above it. For…

Analysis of PDEs · Mathematics 2025-03-26 Mickaël Latocca , Huy Q. Nguyen

We introduce a notion of viscosity solutions for a general class of elliptic-parabolic phase transition problems. These include the Richards equation, which is a classical model in filtration theory. Existence and uniqueness results are…

Analysis of PDEs · Mathematics 2015-06-04 Inwon C. Kim , Norbert Pozar

We consider positive solutions to semilinear elliptic problems with singular nonlinearities, under zero Dirichlet boundary condition. We exploit a refined version of the moving plane method to prove symmetry and monotonicity properties of…

Analysis of PDEs · Mathematics 2016-07-29 Annamaria Canino , Luigi Montoro , Berardino Sciunzi

The paper deals with second order parabolic equations on bounded domains with Dirichlet conditions in arbitrary Euclidean spaces. Their interest comes from being models for describing reaction-diffusion processes in several frameworks. A…

Analysis of PDEs · Mathematics 2018-09-10 Irene Benedetti , Luisa Malaguti , Valentina Taddei

Two-scale models pose a promising approach in simulating reactive flow and transport in evolving porous media. Classically, homogenized flow and transport equations are solved on the macroscopic scale, while effective parameters are…

Analysis of PDEs · Mathematics 2022-02-01 Stephan Gärttner , Peter Knabner , Nadja Ray

We consider parabolic equations with mixed boundary conditions and domain inhomogeneities supported on a lower dimensional hypersurface, enforcing a jump in the conormal derivative. Only minimal regularity assumptions on the domain and the…

Analysis of PDEs · Mathematics 2013-02-05 A. F. M. ter Elst , Martin Meyries , Joachim Rehberg

We investigate existence and nonexistence of stationary stable nonconstant solutions, i.e. patterns, of semilinear parabolic problems in bounded domains of Riemannian manifolds satisfying Robin boundary conditions. These problems arise in…

Analysis of PDEs · Mathematics 2015-07-27 Catherine Bandle , Paolo Mastrolia , Dario D. Monticelli , Fabio Punzo

The flow through a porous medium strongly depends on the boundary conditions, very often assumed to be static. Here, we consider changes in the medium due to swelling and erosion and extend existing Lattice-Boltzmann models to include both.…

In this paper we consider nonlinear parabolic systems with elliptic part which can be also degenerate. We prove optimal error estimates for smooth enough solutions. The main novelty, with respect to previous results, is that we obtain the…

Analysis of PDEs · Mathematics 2020-01-28 Luigi C. Berselli , Michael Růžička

We study the existence and uniqueness of mild and strong solutions of nonlocal nonlinear diffusion problems of $p$-Laplacian type with nonlinear boundary conditions posed in metric random walk spaces. These spaces include, among others,…

Analysis of PDEs · Mathematics 2024-05-24 Marcos Solera , Julián Toledo

We investigate two-phase flow in porous media and derive a two-scale model, which incorporates pore-scale phase distribution and surface tension into the effective behavior at the larger Darcy scale. The free-boundary problem at the pore…

Analysis of PDEs · Mathematics 2023-07-03 Mathis Kelm , Carina Bringedal , Bernd Flemisch