The filtration consolidation problem for media with long-term memory (Q1569353)

The author considers a model in which balance relations for porous medium and filtering liquid are replaced by the condition of consistency of phase deformations. This approach allows to represent the filtration consolidation problem as a Cauchy problem for an operator ordinary differential equation, where the operator itself can be obtained from the solution of a convex variational problem. This, in turn, allows to prove the correctness of this mathematical model important for the filtration consolidation theory. The author applies the results to media with long-term memory.