Global Existence of Solutions of the Gierer-Meinhardt System with Mixed Boundary Conditions

Antwi-Fordjour, Kwadwo; Nkashama, M. N.

doi:10.4236/am.2017.86067

Cited by 4 publications

(2 citation statements)

References 11 publications

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“…In addition, the occurrence of spike clusters has also attracted some scholars' vision [17], [18]. Another significant aspect causing lots of focuses is the property of solutions for this model with different boundary conditions [9], [2]. Furthermore, regarding the pattern formation of reaction-diffusion equations, it is of a high value to consider the major effects of the strength or means of diffusion and reaction on their patterns [1], [22], [3], [21], [6].…”

Section: Introductionmentioning

confidence: 99%

Dynamics and patterns of an activator-inhibitor model with cubic polynomial source

Li¹,

Jiang²

2019

Appl.Math.

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The dynamics of an activator-inhibitor model with general cubic polynomial source is investigated. Without diffusion, we consider the existence, stability and bifurcations of equilibria by both eigenvalue analysis and numerical methods. For the reactiondiffusion system, a Lyapunov functional is proposed to declare the global stability of constant steady states, moreover, the condition related to the activator source leading to Turing instability is obtained in the paper. In addition, taking the production rate of the activator as the bifurcation parameter, we show the decisive effect of each part in the source term on the patterns and the evolutionary process among stripes, spots and mazes. Finally, it is illustrated that weakly linear coupling in the activator-inhibitor model can cause synchronous and anti-phase patterns.

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Section: Introductionmentioning

confidence: 99%

Dynamics and patterns of an activator-inhibitor model with cubic polynomial source

Li¹,

Jiang²

2019

Appl.Math.

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“…Chen et al [10] studied the generalized (singular) Gierer-Meinhardt system with Dirichlet boundary conditions. Recently, Antwi-Fordjour and Nkashama [11] studied the global existence of (1.1). It is well known that it is quite challenging to study the solvability of the equation (1.1) since it does not have a standard variational structure.…”

Section: Introductionmentioning

confidence: 99%