On the global existence and finite time blow-up of shadow systems

DOI10.1016/j.jde.2009.04.009zbMath1203.35049OpenAlexW2063762850MaRDI QIDQ842894

N. E. Zubov

Publication date: 28 September 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2009.04.009

zbMATH Keywords

global existenceGierer-Meinhardt system

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Singular perturbations in context of PDEs (35B25) Blow-up in context of PDEs (35B44)

Related Items (18)

Analysis and asymptotic reduction of a bulk-surface reaction-diffusion model of Gierer-Meinhardt type ⋮ Finite-time blowup of solutions to some activator-inhibitor systems ⋮ Global existence and finite time blow-up of solutions of a Gierer-Meinhardt system ⋮ Dynamical spike solutions in a nonlocal model of pattern formation ⋮ Some results on the Gierer-Meinhardt model with critical exponent \(p - 1 = r\) ⋮ The dynamics of the stochastic shadow Gierer-Meinhardt system ⋮ Blow-up behavior for a degenerate parabolic systems subject to Neumann boundary conditions ⋮ Non-local effects in an integro-PDE model from population genetics ⋮ A remark on global existence of solutions of shadow systems ⋮ Diffusion-Driven Blow-Up for a Nonlocal Fisher-KPP Type Model ⋮ An efficient, nonlinear stability analysis for detecting pattern formation in reaction diffusion systems ⋮ Global dynamics of a competition model with nonlocal dispersal. II: The full system ⋮ Dynamics of shadow system of a singular Gierer-Meinhardt system on an evolving domain ⋮ Well-posedness and fast-diffusion limit for a bulk-surface reaction-diffusion system ⋮ The spatially heterogeneous diffusive rabies model and its shadow system ⋮ Controllability of shadow reaction-diffusion systems ⋮ A Parabolic Free Boundary Problem Arising in a Model of Cell Polarization ⋮ GLOBAL ANALYSIS OF THE SHADOW GIERER-MEINHARDT SYSTEM WITH GENERAL LINEAR BOUNDARY CONDITIONS IN A RANDOM ENVIRONMENT

Cites Work

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• Global existence of solutions of an activator-inhibitor system
• The dynamics of a kinetic activator -- inhibitor system
• Total blow-up versus single point blow-up
• Locating the peaks of least-energy solutions to a semilinear Neumann problem
• Mathematical problems from combustion theory
• Semilinear parabolic equations with prescribed energy
• Stability from the point of view of diffusion, relaxation and spatial inhomogeneity
• Reaction-diffusion systems in the Gierer-Meinhardt theory of biological pattern formation
• Shadow systems and attractors in reaction-diffusion equations
• On the shape of least‐energy solutions to a semilinear Neumann problem
• Activators and Inhibitors in Pattern Formation
• Blow-up in Nonlocal Reaction-Diffusion Equations
• The chemical basis of morphogenesis

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