Analysis and asymptotic reduction of a bulk-surface reaction-diffusion model of Gierer-Meinhardt type
DOI10.3934/CPAA.2022013zbMath1491.35271OpenAlexW4205875845MaRDI QIDQ2128869
Jan-Phillip Bäcker, Matthias Röger
Publication date: 22 April 2022
Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/cpaa.2022013
reaction-diffusion systemsGierer-Meinhardt modelasymptotic reductionPDEs on surfacesbulk-surface systems
Reaction-diffusion equations (35K57) Heat and other parabolic equation methods for PDEs on manifolds (58J35) General biology and biomathematics (92B05) Initial-boundary value problems for second-order parabolic systems (35K51) Pattern formations in context of PDEs (35B36)
Cites Work
- Unnamed Item
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- Global strong solutions for a class of heterogeneous catalysis models
- Hitchhiker's guide to the fractional Sobolev spaces
- Well-posedness and fast-diffusion limit for a bulk-surface reaction-diffusion system
- Global solutions of reaction-diffusion systems
- On the global existence and finite time blow-up of shadow systems
- Partial differential equations. I: Basic theory
- Pattern formation in morphogenesis. Analytical treatment of the Gierer- Meinhardt model on a sphere
- Gagliardo-Nirenberg inequalities and non-inequalities: the full story
- Well-posedness and exponential equilibration of a volume-surface reaction-diffusion system with nonlinear boundary coupling
- Thermomechanical modeling of energy-reaction-diffusion systems, including bulk-interface interactions
- Global existence, uniqueness and stability for nonlinear dissipative bulk-interface interaction systems
- Global existence for a bulk/surface model for active-transport-induced polarisation in biological cells
- A diffuse-interface approach for modelling transport, diffusion and adsorption/desorption of material quantities on a deformable interface
- Diffusion on a curved surface coupled to diffusion in the volume: application to cell biology
- A coupled surface-Cahn–Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes
- Symmetry breaking in a bulk–surface reaction–diffusion model for signalling networks
- Coupled Bulk-Surface Free Boundary Problems Arising from a Mathematical Model of Receptor-Ligand Dynamics
- Global Existence of Solutions to Reaction-Diffusion Systems with Mass Transport Type Boundary Conditions
- Multi-phase Stefan problems for a non-linear one-dimensional model of cell-to-cell adhesion and diffusion
- On the Neumann Problem for Some Semilinear Elliptic Equations and Systems of Activator-Inhibitor Type
- Reaction-diffusion systems in the Gierer-Meinhardt theory of biological pattern formation
- Shadow systems and attractors in reaction-diffusion equations
- Activators and Inhibitors in Pattern Formation
- Dynamical spike solutions in a nonlocal model of pattern formation
- The chemical basis of morphogenesis
- On single interior spike solutions of the Gierer–Meinhardt system: uniqueness and spectrum estimates
- On the dynamics of a non-local parabolic equation arising from the Gierer–Meinhardt system
- The Linear Stability of Symmetric Spike Patterns for a Bulk-Membrane Coupled Gierer--Meinhardt Model
- Nonlinear partial differential equations with applications
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