LARGE-AMPLITUDE OSCILLATIONS AND THEIR THERMODYNAMICS FOR CONTINUA WITH MEMORY

We shall consider a continuum where the pressure depends not only on the specific volume of the mixture but also on its substantial derivatives with respect to time up to the second order. Such a continuum may be called a ''fluid with memory''. A liquid containing small gas bubbles (or a ''bubbly liquid'') is a typical example of these fluids. Oscillations of large amplitude are considered here. It means that the solution depends on ''slow variables'' and periodically on a ''fast variable'', and the amplitude of oscillations is not small. A ''thermodynamic identity'' for averaged (modulated) values is obtained and symmetrical form of modulation equations is found in terms of ''the Gibbs thermodynamic potential''. An explicit formula for the ''entropy'' is found in the case of bubbly liquids.