Finite-time blowup of solutions to some activator-inhibitor systems

DOI10.3934/dcds.2016016zbMath1361.35087OpenAlexW2384024913MaRDI QIDQ321611

Kanako Suzuki, Jacek Zienkiewicz, Grzegorz Karch

Publication date: 14 October 2016

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2016016

zbMATH Keywords

reaction-diffusion systemfinite-time blow-up

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Reaction-diffusion equations (35K57) Blow-up in context of PDEs (35B44)

Related Items (2)

Dynamical spike solutions in a nonlocal model of pattern formation ⋮ Dynamics of shadow system of a singular Gierer-Meinhardt system on an evolving domain

Cites Work

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• Global-in-time behavior of the solution to a Gierer-Meinhardt system
• Unstable patterns in reaction-diffusion model of early carcinogenesis
• On global existence for the Gierer-Meinhardt system
• Global solutions of reaction-diffusion systems
• Global existence of solutions of an activator-inhibitor system
• On the global existence and finite time blow-up of shadow systems
• The dynamics of a kinetic activator -- inhibitor system
• Dynamics of growth and signaling along linear and surface structures in very early tumors
• On a question of blow-up for semilinear parabolic systems
• Diffusion-induced blowup in a nonlinear parabolic system
• Diffusion terms in systems of reaction diffusion equations can lead to blow up
• Boundedness and blow up for the general activator-inhibitor model
• Diffusion-driven blowup of nonnegative solutions to reaction-diffusion-ODE systems.
• Reaction-Difusion Model of Early Carcinogenesis: The Effects of Influx of Mutated Cells
• Density-dependent quiescence in glioma invasion: instability in a simple reaction–diffusion model for the migration/proliferation dichotomy
• Reaction-diffusion systems in the Gierer-Meinhardt theory of biological pattern formation
• Blowup in Reaction-Diffusion Systems with Dissipation Of Mass
• The chemical basis of morphogenesis
• Receptor-Based Models with Diffusion-Driven Instability for Pattern Formation in Hydra
• Blowup in Reaction-Diffusion Systems with Dissipation of Mass
• On the Role of Basic Production Terms in an Activator-Inhibitor System Modeling Biological Pattern Formation
• Reaction versus diffusion: blow-up induced and inhibited by diffusivity

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