On the spatial behaviour in dynamics of porous elastic mixtures

TL;DR

This paper investigates the spatial and temporal dynamics of porous elastic mixtures, establishing decay estimates and energy distribution properties without prior assumptions, advancing understanding of their behavior over time and space.

Contribution

It introduces a novel method for determining the domain of influence and proves a new uniqueness theorem for porous elastic mixtures without a priori assumptions.

Findings

Established spatial decay estimates of Saint-Venant type

Proved asymptotic equipartition of total energy

Derived a uniqueness theorem free of assumptions at infinity

Abstract

In this paper we study the spatial and temporal behaviour of the dynamic processes in porous elastic mixtures. For the spatial behaviour we use the time-weighted surface power function method in order to obtain a more precisely determination of the domain of influence and we establish spatial decay estimates of Saint-Venant type with time-independent decay rate for the inside of the domain of influence. For the asymptotic temporal behaviour we use the Cesaro means associated with the kinetic and strain energies and establish the asymptotic equipartition of the total energy. A uniqueness theorem is proved for finite and infinite bodies and we note that it is free of any kind of a priori assumptions of the solutions at infinity.