The Aronson-Bénilan estimate in Lebesgue spaces
From MaRDI portal
Publication:6172264
DOI10.4171/aihpc/43zbMath1518.35157arXiv2007.15267MaRDI QIDQ6172264
Giulia Bevilacqua, Markus Schmidtchen, Perthame, Benoît
Publication date: 19 July 2023
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2007.15267
PDEs in connection with biology, chemistry and other natural sciences (35Q92) Degenerate parabolic equations (35K65) A priori estimates in context of PDEs (35B45)
Related Items (1)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Differential equations with singular fields
- Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds
- Continuity of the temperature in the two-phase Stefan problem
- Modelling the role of cell-cell adhesion in the growth and development of carcinomas
- A hierarchy of cancer models and their mathematical challenges
- Bifurcation analysis for a mean field modelling of tumor and immune system competition
- Incompressible limit of a mechanical model for tissue growth with non-overlapping constraint
- Boundary layer formation in the transition from the porous media equation to a Hele-Shaw flow.
- Incompressible limit for a two-species tumour model with coupling through Brinkman's law in one dimension
- Incompressible limit of a continuum model of tissue growth with segregation for two cell populations
- Incompressible limit of a continuum model of tissue growth for two cell populations
- A multiscale mathematical model of avascular tumor growth to investigate the therapeutic benefit of anti-invasive agents
- Global existence theorem for a model governing the motion of two cell populations
- Incompressible limit for a two-species model with coupling through Brinkman's law in any dimension
- Free boundary limit of a tumor growth model with nutrient
- Derivation of a Hele-Shaw type system from a cell model with active motion
- Hele-Shaw limit for a system of two reaction-(Cross-)diffusion equations for living tissues
- Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications
- Individual-based and continuum models of growing cell populations: a comparison
- A Hele-Shaw problem for tumor growth
- The Hele-Shaw asymptotics for mechanical models of tumor growth
- Regularity properties of flows through porous media: The interface
- Optimal regularity in time and space for the porous medium equation
- Optimal regularity for the porous medium equation
- Incompressible limit of a mechanical model of tumour growth with viscosity
- Computational Modeling of Solid Tumor Growth: The Avascular Stage
- Asymptotic Behaviour of Solutions of a Multidimensional Moving Boundary Problem Modeling Tumor Growth
- ON THE FOUNDATIONS OF CANCER MODELLING: SELECTED TOPICS, SPECULATIONS, AND PERSPECTIVES
- Stability and instability of Liapunov-Schmidt and Hopf bifurcation for a free boundary problem arising in a tumor model
- LINEAR EQUATIONS OF THE SECOND ORDER OF PARABOLIC TYPE
- Continuity of the Density of a Gas Flow in a Porous Medium
- Regularity of the Free Boundary for the One-Dimensional Flow of Gas in a Porous Medium
- A selfsimilar solution to the focusing problem for the porous medium equation
- Splitting Schemes and Segregation in Reaction Cross-Diffusion Systems
- Porous medium equation to Hele-Shaw flow with general initial density
- Regularizing Effects for u t = Δϕ(u)
- The focusing problem for the radially symmetric porous medium equation
- Toward Understanding the Boundary Propagation Speeds in Tumor Growth Models
- Analysis of Cross-Diffusion Systems for Fluid Mixtures Driven by a Pressure Gradient
- A two-species hyperbolic–parabolic model of tissue growth
- Regularity Propeties of Flows Through Porous Media
- Regularity Properties of Flows Through Porous Media: A Counterexample
- Models for the Growth of a Solid Tumor by Diffusion
- DIFFUSION FROM AN INSTANTANEOUS POINT SOURCE WITH A CONCENTRATION-DEPENDENT COEFFICIENT
- Nonlinear modelling of cancer: bridging the gap between cells and tumours
- Convergence of the porous media equation to Hele-Shaw
This page was built for publication: The Aronson-Bénilan estimate in Lebesgue spaces
