nonlocal and nonlinear evolution equation
two local spatially homogeneous equilibria
Stability of planar fronts for a non-local phase kinetics equation with a conservation law in \(D \leq 3\)
The authors study a nonlocal and nonlinear evolution equation, in a cylinder, describing the dynamics of a local magnetization process. Here, a basic tool is represented by the Gates-Penrose-Lebowitz free energy functional defined on the measurable functions of the cylinder through which the considered equation is written in a gradient flow form. It is shown that for sub-critical temperatures there are two local spatially homogeneous equilibria. A stability result for the planar fronts is established.
scientific article; zbMATH DE number 6050827