On the dynamics of a non-local parabolic equation arising from the Gierer–Meinhardt system

DOI10.1088/1361-6544/AA64B2zbMath1372.35138arXiv1605.04083OpenAlexW2596977676MaRDI QIDQ5268491

Nikos I. Kavallaris, Takashi Suzuki

Publication date: 20 June 2017

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.04083

zbMATH Keywords

blow-upnonlocal equationsTuring instabilityGierer-Meinhardt model

Mathematics Subject Classification ID

Blow-up in context of PDEs (35B44) Integro-partial differential equations (35R09) Initial-boundary value problems for second-order parabolic systems (35K51) Pattern formations in context of PDEs (35B36) Mathematical biology in general (92Bxx)

Related Items (10)

Analysis and asymptotic reduction of a bulk-surface reaction-diffusion model of Gierer-Meinhardt type ⋮ Blowup solutions for the nonlocal shadow limit model of a singular Gierer-Meinhardt system with critical parameters ⋮ Global existence, finite time blow-up, and vacuum isolating phenomenon for a class of thin-film equation ⋮ Steady state solutions for the Gierer-Meinhardt system in the whole space ⋮ Diffusion-Driven Blow-Up for a Nonlocal Fisher-KPP Type Model ⋮ Global existence and blow-up of solutions to a nonlocal parabolic equation with singular potential ⋮ Global asymptotical behavior and some new blow-up conditions of solutions to a thin-film equation ⋮ Diffusion-induced blowup solutions for the shadow limit model of a singular Gierer–Meinhardt 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

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