Abstract
In this paper, we study the spatial and temporal behavior of dynamic processes in porous elastic mixtures. For the spatial behavior, we use the time-weighted surface power function method in order to obtain a more precise determination of the domain of influence and establish spatial-decay estimates of the Saint-Venant type with respect to time-independent decay rate for the inside of the domain of influence. For the asymptotic temporal behavior, we use the Cesáro 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 on the solutions at infinity.
Similar content being viewed by others
REFERENCES
C. Truesdell and R Toupin, “The classical field theories,” in: S. Flügge (editor), Handbuch der Physik, Vol. 3, Springer, Berlin (1960).
P. Kelly, “A reacting continuum,” Int. J. Eng. Sci., 2, 129–153 (1964).
A. C. Eringen and J. D. Ingram, “A continuum theory of chemically reacting media I,” Int. J. Eng. Sci., 3, 197–212 (1965).
J. D. Ingram and A. C. Eringen, “A continuum theory of chemically reacting media II. Constitutive equations of reacting fluid mixtures,” Int. J. Eng. Sci., 4, 289–322 (1967).
A. E. Green and P. M. Naghdi, “A dynamical theory of interacting continuum,” Int. J. Eng. Sci., 3, 231–241 (1965).
A. E. Green and P. M. Naghdi, “A note on mixtures,” Int. J. Eng. Sci., 6, 631–635 (1968).
I. Müller, “A thermodynamic theory of mixtures of fluids,” Arch. Ration. Mech. Anal., 28, 1–39 (1968).
N. Dunwoody and I. Müller, “A thermodynamic theory of two chemically reacting ideal gases with different temperatures,” Arch. Ration. Mech. Anal., 29, 344–369 (1968).
A. Bedford and D. S. Drumheller, “Theory of immiscible and structured mixtures,” Int. J. Eng. Sci., 21, 863–960 (1983).
D. Ieşan,“On the theory of mixtures of elastic solids,” J. Elast., 35, 251–268 (1994).
J. W. Nunziato and S. C. Cowin, “A nonlinear theory of elastic materials with voids,” Arch. Ration. Mech. Anal., 72, 175–201 (1979).
M. A. Goodman and S. C. Cowin, “A continuum theory for granular materials,” Arch. Ration. Mech. Anal., 44, 249–266 (1972).
D. S. Drumheller, “The theoretical treatment of a porous solid using a mixture theory,” Int. J. Solids Struct., 14, 441–456 (1979).
S. Chiriţă and M. Ciarletta, “Time-weighted surface power function method for the study of spatial behavior in dynamics of continuum,” Eur. J. Mech. A/Solids, 18, 915–933 (1999).
W. A. Day, “Means and autocorrelations in elastodynamics,” Arch. Ration. Mech. Anal., 73, 243–256 (1980).
H. A. Levine, “An equipartition of energy theorem for weak solutions of evolutionary equations in Hilbert space: The Lagrange identity method,” J. Different. Equat., 24, 197–210 (1974).
A. Bedford and M. Stern, “A multi-continuum theory for composite elastic materials,” Acta Mech., 14, 85–102 (1972).
M. A. Gurtin, “Linear theory of elasticity,” in: S. Flügge (editor), Handbuch der Physik, VIa/2, Springer, Berlin (1972), pp. 1–295.
I. Hlavácek and J. Necas, “On inequalities of Korn's type,” Arch. Ration. Mech. Anal., 36, 305–334 (1970).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ciarletta, M., Iovane, G. & Passarella, F. On the Spatial and Temporal Behavior in Dynamics of Porous Elastic Mixtures. Ukrainian Mathematical Journal 54, 647–670 (2002). https://doi.org/10.1023/A:1021091512888
Issue Date:
DOI: https://doi.org/10.1023/A:1021091512888