On the Existence of High Multiplicity Interfaces
On the Existence of High Multiplicity Interfaces
In many singularly perturbed Ginzburg-Landau type partial differential equations, such as the Allen-Cahn equation, the nonlocal Allen-Cahn equation, and the Cahn-Hilliard equation, the question arises whether or not the limiting interfaces can have high multiplicity.In other words, do there exist solutions of these PDE's with many transition layers (where the …