A Symmetry-Breaking Bifurcation Problem
In this problem, we solve the nonlinear elliptic problem
-0.1 Laplace u + u =\lambda exp(u) on the unit square with
homogeneous Neumann boundary conditions.
This problem illustrates the continuation options available in
PLTMG. The continuation is carried out on a uniform coarse mesh.
Here is a picture of the
continuation path.
Points marked blue are limit (turning) points. Those marked red are
bifurcation points. All marked points are computed in the continuation
process. The solution on the primary branch is constant.
On the secondary branch the solution has less symmetry. The left picture
is near the bifurcation point, while the right is near the end of the
computed portion of the secondary branch.
On the tertiary branch the solution has even less symmetry. The left picture
is near the bifurcation point, while the right is near the end of the
computed portion of the tertiary branch.
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