EVOLUTION OF A MICROSTRUCTURE - A CONVEXIFIED MODEL

It is known that, in a steady-state case, the variational principle of minimal non-convex potential energy creates a microstructure. This paper tries to formulate evolution of such microstructure on a basis of an energy variational principle (of the Hamilton type) involving a kinetic and a Rayleigh dissipative energies with the generalized impulse respecting a 'convexified' geometry. The existence of a solution is proved, using an approximation by a semi-discretization in time. Some quantitative properties are investigated, too