Dynamics of metastable localized patterns and its application to the interaction of spike solutions for the Gierer-Meinhardt systems in two spatial dimensions
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Publication:698392
DOI10.1007/BF03167453zbMath1029.35130WikidataQ121689719 ScholiaQ121689719MaRDI QIDQ698392
Publication date: 29 January 2004
Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)
pattern formationreaction-diffusion systemTuring instabilityGierer-Meinhardt modelinteraction of spike solutions
Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02)
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Stable boundary spike clusters for the two-dimensional Gierer-Meinhardt system, Spot self-replication and dynamics for the Schnakenburg model in a two-dimensional domain, Stable spike clusters for the precursor Gierer-Meinhardt system in \(\mathbb {R}^2\), Stable spike clusters for the one-dimensional Gierer–Meinhardt system, The dynamics of pulse solutions for reaction diffusion systems on a star shaped metric graph with the Kirchhoff's boundary condition, Dynamics and interactions of spikes on smoothly curved boundaries for reaction-diffusion systems in 2D, Interaction of non-radially symmetric camphor particles, Heterogeneity-induced effects for pulse dynamics in FitzHugh-Nagumo-type systems, The Gierer-Meinhardt system on a compact two-dimensional Riemannian manifold: Interaction of Gaussian curvature and Green's function, Stable spike clusters on a compact two-dimensional Riemannian manifold, Spike solutions for a mass conservation reaction-diffusion system
Cites Work
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- On the boundary spike layer solutions to a singularly perturbed Neumann problem
- On the structure of the conformal Gaussian curvature equation on \({\mathbb{R}}^ 2\)
- On the elliptic equation \(\Delta u+Ku^{(n+2)/(n-2)}=0\) and related topics
- Stationary solutions for the Cahn-Hilliard equation
- On the interior spike layer solutions to a singularly perturbed Neumann problem
- Multi-peak solutions for a semilinear Neumann problem involving the critical Sobolev exponent
- Locating the peaks of least-energy solutions to a semilinear Neumann problem
- Slow dynamics for the Cahn-Hilliard equation in higher space dimensions: The motion of bubbles
- Multi-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability.
- Multipeak solutions for a semilinear Neumann problem
- Multiple interior peak solutions for some singularly perturbed Neumann problems.
- Point condensation generated by a reaction-diffusion system in axially symmetric domains
- On the construction of single-peaked solutions to a singularly perturbed semilinear Dirichlet problem
- Equilibria with many nuclei for the Cahn-Hilliard equation
- Multiple spike layers in the shadow Gierer-Meinhardt system: Existence of equilibria and the quasi-invariant manifold
- Multiple boundary peak solutions for some singularly perturbed Neumann problems
- Uniqueness of the positive solution of \(\Delta u+f(u)=0\) in an annulus
- On the shape of least‐energy solutions to a semilinear Neumann problem
- On the interior spike solutions for some singular perturbation problems
- Existence, stability and metastability of point condensation patterns generated by the Gray-Scott system
- On a singularly perturbed equation with neumann boundary condition
- The chemical basis of morphogenesis
- Metastable Bubble Solutions for the Allen-Cahn Equation with Mass Conservation
- On single interior spike solutions of the Gierer–Meinhardt system: uniqueness and spectrum estimates
- On the location and profile of spike‐layer solutions to singularly perturbed semilinear dirichlet problems
- An Asymptotic Analysis of Localized Solutions for Some Reaction‐Diffusion Models in Multidimensional Domains
- A Metastable Spike Solution for a Nonlocal Reaction-Diffusion Model
- On the role of distance function in some singular perturbation problems
- Pattern formations in two-dimensional Gray-Scott model: Existence of single-spot solutions and their stability
- Slow dynamics of interior spikes in the shadow Gierer-Meinhardt system
- The motion of weakly interacting pulses in reaction-diffusion systems
