A singular Gierer-Meinhardt system with different source terms

. A P ] 2 6 N ov 2 00 6 A singular Gierer - Meinhardt system with different source terms

We study the existence and nonexistence of classical solutions to a general Gierer-Meinhardt system with Dirichlet boundary condition. The main feature of this paper is that we are concerned with a model in which both the activator and the inhibitor have different sources given by general nonlinearities. Under some additional hypotheses and in case of pure powers in nonlinearities, regularity a...

Pulses in a Gierer-Meinhardt Equation with a Slow Nonlinearity

In this paper, we study in detail the existence and stability of localized pulses in a GiererMeinhardt equation with an additional ‘slow’ nonlinearity. This system is an explicit example of a general class of singularly perturbed, two component reaction-diffusion equations that goes significantly beyond wellstudied model systems such as Gray-Scott and Gierer-Meinhardt. We investigate the existe...

Steady-state solutions for Gierer-Meinhardt type systems with Dirichlet boundary condition

This paper is concerned with the following Gierer-Meinhardt type systems subject to Dirichlet boundary conditions    ∆u− αu + u p vq + ρ(x) = 0, u > 0 in Ω, ∆v − βv + u r vs = 0, v > 0 in Ω, u = 0, v = 0 on ∂Ω, where Ω ⊂ R (N ≥ 1) is a smooth bounded domain, ρ(x) ≥ 0 in Ω and α, β ≥ 0. We are mainly interested in the case of different source terms, that is, (p, q) 6= (r, s). Under approp...

Stability of spikes in the shadow Gierer-Meinhardt system with Robin boundary conditions Short title: Gierer-Meinhardt system with Robin boundary conditions

Spikes for the Gierer-meinhardt System in Two Dimensions: the Strong Coupling Case

Numerical computations often show that the Gierer-Meinhardt system has stable solutions which display patterns of multiple interior peaks (often also called spots). These patterns are also frequently observed in natural biological systems. It is assumed that the diffusion rate of the activator is very small and the diffusion rate of the inhibitor is finite (this is the so-called strong-coupling...