A Coupled Ligand-Receptor Bulk-Surface System on a Moving Domain: Well Posedness, Regularity, and Convergence to Equilibrium
From MaRDI portal
Publication:4608167
DOI10.1137/16M110808XzbMath1390.35144arXiv1612.03007MaRDI QIDQ4608167
Charles M. Elliott, Amal Alphonse, Joana Terra
Publication date: 16 March 2018
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1612.03007
Reaction-diffusion equations (35K57) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Cell biology (92C37) Moving boundary problems for PDEs (35R37) PDEs on manifolds (35R01)
Related Items
Global well-posedness for volume–surface reaction–diffusion systems ⋮ Homogenization of a reaction-diffusion-advection problem in an evolving micro-domain and including nonlinear boundary conditions ⋮ Function spaces, time derivatives and compactness for evolving families of Banach spaces with applications to PDEs ⋮ An evolving space framework for Oseen equations on a moving domain ⋮ Multiscale Analysis and Simulation of a Signaling Process With Surface Diffusion ⋮ Mini-workshop: PDE models of motility and invasion in active biosystems. Abstracts from the mini-workshop held October 22--28, 2017 ⋮ A generalization of the Aubin-Lions-Simon compactness lemma for problems on moving domains ⋮ Moving boundary problems ⋮ Analysis of a bulk-surface thermistor model for large-area organic LEDs ⋮ Quasilinear parabolic equations with first order terms and \(L^1\)-data in moving domains ⋮ Cahn–Hilliard equations on an evolving surface
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Parabolic optimal control problems on evolving surfaces subject to point-wise box constraints on the control-theory and numerical realization
- Mathematical modelling and computational study of two-dimensional and three-dimensional dynamics of receptor-ligand interactions in signalling response mechanisms
- On some linear parabolic PDEs on moving hypersurfaces
- Exponential decay towards equilibrium and global classical solutions for nonlinear reaction-diffusion systems
- Functional spaces for the theory of elliptic partial differential equations. Transl. from the French by Reinie Erné
- Degenerate parabolic equations
- Turing instabilities in a mathematical model for signaling networks
- A computational method for the coupled solution of reaction-diffusion equations on evolving domains and manifolds: application to a model of cell migration and chemotaxis
- Global solutions of reaction-diffusion systems
- Stability analysis of reaction-diffusion models on evolving domains: the effects of cross-diffusion
- Well-posedness and exponential equilibration of a volume-surface reaction-diffusion system with nonlinear boundary coupling
- Mathematical tools for the study of the incompressible Navier-Stokes equations and related models
- An ALE ESFEM for solving PDEs on evolving surfaces
- Cross-diffusion-driven instability for reaction-diffusion systems: analysis and simulations
- An abstract framework for parabolic PDEs on evolving spaces
- Explicit exponential convergence to equilibrium for nonlinear reaction-diffusion systems with detailed balance condition
- Optimal \(L^{p}\)- \(L^{q}\)-estimates for parabolic boundary value problems with inhomogeneous data
- Exponential decay toward equilibrium via entropy methods for reaction-diffusion equations
- Signaling networks and cell motility: a computational approach using a phase field description
- Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus
- Local behavior of solutions of quasilinear parabolic equations
- Entropy Methods for Diffusive Partial Differential Equations
- Symmetry breaking in a bulk–surface reaction–diffusion model for signalling networks
- Exponential Convergence to Equilibrium for Nonlinear Reaction-Diffusion Systems Arising in Reversible Chemistry
- A Stefan problem on an evolving surface
- Coupled Bulk-Surface Free Boundary Problems Arising from a Mathematical Model of Receptor-Ligand Dynamics
- Global Existence for Semilinear Parabolic Systems
- Shapes and Geometries
- Vector-valued Laplace Transforms and Cauchy Problems
- Harnack's Inequality for Degenerate and Singular Parabolic Equations
- Transport relations for surface integrals arising in the formulation of balance laws for evolving fluid interfaces
- Finite elements on evolving surfaces
- A trace finite element method for a class of coupled bulk-interface transport problems
- Coupled system of reaction-diffusion equations and applications in carrier facilitated diffusion
- THE BEST-CONSTANT PROBLEM FOR A FAMILY OF GAGLIARDO–NIRENBERG INEQUALITIES ON A COMPACT RIEMANNIAN MANIFOLD
- Maximal regularity for parabolic equations with inhomogeneous boundary conditions in Sobolev spaces with mixed $L_p$-norm
- Cross-Diffusion Limit for a Reaction-Diffusion System with Fast Reversible Reaction
- Finite element methods for surface PDEs
- Inhomogeneous parabolic Neumann problems
- On the Green's function for second order parabolic differential equations with discontinuous coefficients