Nonlinear parabolic equations, relaxation and roughness. (Q1415373)

The authors consider a related equation of Ginzburg-Landau type, extended for the kinetic depinning transition. They study this equation for the variable in \(\mathbb{R}^5\) or \(\mathbb{R}^9\) or \(\mathbb{R}^{13}.\) The physical importance of these cases is related to the following problems: 1) interaction of a particle with the initial atom of a chain of atoms, 2) interaction with the initial atom of a chain of atoms and a hole (antiparticle) related to the previous position of an atom in the crystallographic lattice, 3) interaction with a system of atoms.