Qualitative behavior and traveling waves for flux-saturated porous media equations arising in optimal mass transportation

DOI10.1016/J.NA.2015.12.021zbMath1386.35198OpenAlexW2280994827MaRDI QIDQ272711

F. Blanchet-Sadri, M. Dambrine

Publication date: 20 April 2016

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2015.12.021

zbMATH Keywords

traveling wavesflux limitationporous media equations

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Reaction-diffusion equations (35K57) Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Flows in porous media; filtration; seepage (76S05) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Continuation and prolongation of solutions to PDEs (35B60) Traveling wave solutions (35C07) Singular parabolic equations (35K67) Pattern formations in context of PDEs (35B36)

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Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision ⋮ Wavefronts in traffic flows and crowds dynamics ⋮ The Fisher-KPP problem with doubly nonlinear diffusion ⋮ EnVarA-FEM for the flux-limited porous medium equation ⋮ Bistable reaction equations with doubly nonlinear diffusion ⋮ Traveling waves for a Fisher-type reaction–diffusion equation with a flux in divergence form ⋮ Singular patterns in Keller–Segel-type models ⋮ Anisotropic tempered diffusion equations ⋮ Strong solutions to a parabolic equation with linear growth with respect to the gradient variable ⋮ Cross-diffusion and traveling waves in porous-media flux-saturated Keller–Segel models ⋮ Singular Traveling Waves and Non-linear Reaction-Diffusion Equations ⋮ Qualitative behaviour for flux-saturated mechanisms: travelling waves, waiting time and smoothing effects ⋮ On sonic hedgehog morphogenic action and finite propagation speed models ⋮ Saturated fronts in crowds dynamics ⋮ A multiscale view of nonlinear diffusion in biology: From cells to tissues

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