Add to ORKGBoundary conditions may induce subtle effects on the genericity of bifurcation problems. The group of transformations that leave the domain invariant does not necessarily contain all the symmetries of the problem. We give a detailed description of how this phenomenon occurs for elliptic PDEs (in particular steady reaction-diffusion equations) with Neumann boundary conditions on n-dimensional rectangles. The generic bifurcation equations for mode interactions are given in the appropriate symmetry context. We observe that the form of the equations does not depend on the dimension of the domain. With a suitable interpretation and some extra minor considerations, the classification of Armbruster and Dangelmayr for the 1-dimensional case applies...
In this paper, we use rigorous numerics to compute several global smooth branches of steady states f...
We show that the elliptic problem $\Delta u+f(u)=0$ in $\mathbb{R}^N$, $N\ge 1$, with $f\in C^1(\mat...
In this article we present a computational framework for isolating spatial patterns arising in the s...
Fujii, Mimura, and Nishiura [1985] and Armbruster and Dangelmayr [1986, 1987] have observed that rea...
We consider a reaction-di#usion equation with Neumann boundary conditions and show that solutions t...
Bifurcation problems with the symmetry group Z(2) + Z(2) of the rectangle are common in applied scie...
We set up a singularity-theoretic framework for classifying one-parameter steady-state bifurcations ...
summary:We study a parameter depending semilinear elliptic PDE on a rectangle with Signorini boundar...
We consider systems of partial differential equations equivariant under the Euclidean group E(n) and...
It is now well known that bifurcation problems arising from elliptic PDEs on finite domains may poss...
Abstract In this paper, we are concerned with a homogeneous reaction–diffusion Atkinson oscillator s...
Abstract. We study the bifurcation of radially symmetric solutions of Au+f(u)=O on n-balls, into asy...
We are concerned with the global bifurcation analysis of positive solutions to free boundary proble...
summary:We consider a reaction-diffusion system of the activator-inhibitor type with boundary condit...
AbstractWe consider a reaction–diffusion system of activator–inhibitor or substrate-depletion type w...
In this paper, we use rigorous numerics to compute several global smooth branches of steady states f...
We show that the elliptic problem $\Delta u+f(u)=0$ in $\mathbb{R}^N$, $N\ge 1$, with $f\in C^1(\mat...
In this article we present a computational framework for isolating spatial patterns arising in the s...
Fujii, Mimura, and Nishiura [1985] and Armbruster and Dangelmayr [1986, 1987] have observed that rea...
We consider a reaction-di#usion equation with Neumann boundary conditions and show that solutions t...
Bifurcation problems with the symmetry group Z(2) + Z(2) of the rectangle are common in applied scie...
We set up a singularity-theoretic framework for classifying one-parameter steady-state bifurcations ...
summary:We study a parameter depending semilinear elliptic PDE on a rectangle with Signorini boundar...
We consider systems of partial differential equations equivariant under the Euclidean group E(n) and...
It is now well known that bifurcation problems arising from elliptic PDEs on finite domains may poss...
Abstract In this paper, we are concerned with a homogeneous reaction–diffusion Atkinson oscillator s...
Abstract. We study the bifurcation of radially symmetric solutions of Au+f(u)=O on n-balls, into asy...
We are concerned with the global bifurcation analysis of positive solutions to free boundary proble...
summary:We consider a reaction-diffusion system of the activator-inhibitor type with boundary condit...
AbstractWe consider a reaction–diffusion system of activator–inhibitor or substrate-depletion type w...
In this paper, we use rigorous numerics to compute several global smooth branches of steady states f...
We show that the elliptic problem $\Delta u+f(u)=0$ in $\mathbb{R}^N$, $N\ge 1$, with $f\in C^1(\mat...
In this article we present a computational framework for isolating spatial patterns arising in the s...