6 citations · 16 across the 8 of their papers we have counts for
8 papers
Existence and Stability of a Boundary Layer with an Interior Spike in the Singularly Perturbed Shadow Gierer-Meinhardt System
Daniel Gomez, Juncheng Wei
The singularly perturbed Gierer-Meinhardt (GM) system in a bounded -dimensional domain () is known to exhibit boundary layer (BL) solutions for a non-zero activator flu…
First Hitting Time of a One-Dimensional Levy Flight to Small Targets
Daniel Gomez, Sean D Lawley
First hitting times (FHTs) describe the time it takes a random "searcher" to find a "target" and are used to study timescales in many applications. FHTs have been well-studied for…
Spike Solutions to the Supercritical Fractional Gierer-Meinhardt System
Daniel Gomez, Markus De Medeiros, Jun-cheng Wei +1
Localized solutions are known to arise in a variety of singularly perturbed reaction-diffusion systems. The Gierer-Meinhardt (GM) system is one such example and has been the focus…
Multi-Spike Solutions to the Fractional Gierer-Meinhardt System in a One-Dimensional Domain
Daniel Gomez, Juncheng Wei, Wen Yang
In this paper we consider the existence and stability of multi-spike solutions to the fractional Gierer-Meinhardt model with periodic boundary conditions. In particular we rigorous…
An Asymptotic Analysis of Localized 3-D Spot Patterns for Gierer-Meinhardt Model: Existence, Linear Stability and Slow Dynamics
Daniel Gomez, Michael J. Ward, Juncheng Wei
Localized spot patterns, where one or more solution components concentrates at certain points in the domain, are a common class of localized pattern for reaction-diffusion systems,…
Multi-Spike Patterns in the Gierer-Meinhardt System with a Non-Zero Activator Boundary Flux
Daniel Gomez, Juncheng Wei
The structure, linear stability, and dynamics of localized solutions to singularly perturbed reaction-diffusion equations has been the focus of numerous rigorous, asymptotic, and n…
The Stability and Dynamics of Localized Spot Patterns for a Bulk-Membrane Coupled Brusselator Model
Daniel Gomez
We consider a bulk-membrane-coupled partial differential equation in which a single diffusion equation posed within the unit ball is coupled to a two-component reaction diffusion e…
The Linear Stability of Symmetric Spike Patterns for a Bulk-Membrane Coupled Gierer-Meinhardt Model
Daniel Gomez, Michael J. Ward, Juncheng Wei
We analyze a coupled bulk-membrane PDE model in which a scalar linear 2-D bulk diffusion process is coupled through a linear Robin boundary condition to a two-component 1-D reactio…