Open AccessOn the time decay for the MGT-type porosity problems
Author(s) -
Jacobo Baldonedo,
José R. Fernández,
R. Quintanilla
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2022009
Subject(s) - porosity , dissipation , porous medium , hyperviscosity , viscosity , mathematics , term (time) , exponential decay , relaxation (psychology) , polynomial , type (biology) , mathematical analysis , physics , thermodynamics , materials science , composite material , quantum mechanics , blood viscosity , medicine , psychology , social psychology , cardiology , ecology , biology
In this work we study three different dissipation mechanisms arising in the so-called Moore-Gibson-Thompson porosity. The three cases correspond to the MGT-porous hyperviscosity (fourth-order term), the MGT-porous viscosity (second-order term) and the MGT-porous weak viscosity (zeroth-order term). For all the cases, we prove that there exists a unique solution to the problem and we analyze the resulting point spectrum. We also show that there is an exponential energy decay for the first case, meanwhile for the second and third case only a polynomial decay is found. Finally, we present some one-dimensional numerical simulations to illustrate the behaviour of the discrete energy for each case.