Standing waves in the FitzHugh-Nagumo system and a problem in combinatorial geometry
From MaRDI portal
Publication:852347
DOI10.1007/s00209-006-0952-8zbMath1251.35010OpenAlexW2024353155MaRDI QIDQ852347
Matthias Winter, Wei, Juncheng
Publication date: 29 November 2006
Published in: Mathematische Zeitschrift (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00209-006-0952-8
Asymptotic behavior of solutions to PDEs (35B40) Biochemistry, molecular biology (92C40) A priori estimates in context of PDEs (35B45) Developmental biology, pattern formation (92C15) Boundary value problems for second-order elliptic systems (35J57)
Related Items
Fitzhugh-Nagumo system with zero mass and critical growth, Traveling waves for the Fitzhugh-Nagumo system on an infinite channel, Existence of solution for a class of activator–inhibitor systems, Existence of semi-nodal solution for a class of Fitzhugh-Nagumo type system, Existence of solutions for critical Fractional FitzHugh–Nagumo type systems, Cluster solutions for the Fitzhugh-Nagumo system with Neumann boundary conditions, Monostable-type travelling wave solutions of the diffusive FitzHugh-Nagumo-type system in \(\mathbb{R}^N\), A variational approach for standing waves of Fitzhugh-Nagumo type systems, Synchronization of FitzHugh-Nagumo reaction-diffusion systems via one-dimensional linear control law
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Spatially periodic and aperiodic multi-pulse patterns in the one-dimensional Gierer-Meinhardt equation
- Exact multiplicity of positive solutions for a class of semilinear problems
- Stationary solutions for the Cahn-Hilliard equation
- A positive solution on \(\mathbb{R}^N\) to a system of elliptic equations of FitzHugh-Nagumo type
- Standing pulse solutions for the FitzHugh-Nagumo equations
- Multi-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability.
- Multipeak solutions for a singularly perturbed Neumann problem
- Multiple interior peak solutions for some singularly perturbed Neumann problems.
- Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
- On the bifurcation curve for an elliptic system of FitzHugh-Nagumo type
- Existence and instability of spike layer solutions to singular perturbation problems
- On stable nonconstant stationary solutions and mesoscopic patterns for FitzHugh-Nagumo equations in higher dimensions.
- Multi-bump ground states of the Gierer-Meinhardt system in \(\mathbb R^2\).
- A minimization problem associated with elliptic systems of FitzHugh--Nagumo type
- Equilibria with many nuclei for the Cahn-Hilliard equation
- Critical points of a singular perturbation problem via reduced energy and local linking
- 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
- Symmetric and asymmetric multiple clusters in a reaction-diffusion system
- THE GIERER & MEINHARDT SYSTEM: THE BREAKING OF HOMOCLINICS AND MULTI-BUMP GROUND STATES
- The Problem of the Thirteen Spheres
- Standing Wave Solutions for a System Derived from the Fitzhugh–Nagumo Equations for Nerve Conduction
- A Maximum Principle for an Elliptic System and Applications to Semilinear Problems
- Stability of Singularly Perturbed Solutions to Systems of Reaction-Diffusion Equations
- On steady state solutions of a system of reaction-diffusion equations from biology
- A boundary layer solution to a semilinear elliptic system of FitzHugh-Nagumo type
- Finite dimensional dynamics and interfaces intersecting the boundary: Equilibria and the quasi-invariant manifold
- A note on asymptotic uniqueness for some nonlinearities which change sign
- On Multiple Mixed Interior and Boundary Peak Solutions for Some Singularly Perturbed Neumann Problems
- Solutions with internal jump for an autonomous elliptic system of FitzHugh–Nagumo type
- On the location and profile of spike‐layer solutions to singularly perturbed semilinear dirichlet problems
- Interior and Boundary Peak Solutions for a Mixed Boundary Value Problem
- Existence and uniqueness of solutions on bounded domains to a FitzHugh-Nagumo type elliptic system.
