Existence and uniqueness results to a phase transition model based on microscopic accelerations and movements

Abstract

Microscopic movements are responsible for the phase transition at the macroscopic level. The power of the microscopic accelerations of these motions is not neglected, as opposed to some previous works, in the derivation of phase transition models accounting for strong dissipation or irreversible phenomena. Such models lead to nonlinear parabolic–hyperbolic systems. Some existence and uniqueness results are established, through fixed point and regularization arguments, for related Cauchy–Neumann problems.