Abstract
We study a class of symmetric systems of linear partial differential equations which involve tensor functions relating tensor spaces on a three dimensional vector space, on the real field, equipped with an inner product. These systems arise by coupling certain simpler symmetric systems studied in a previous paper. In order to investigate some questions, related to constitutive equations for bodies of the differential type, certain classes of physically privileged solutions are characterized for some of the aforementioned systems.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
B. Finzi -M. Pastori,Calcolo tensoriale e applicazioni, second edition, Zanichelli, Bologna (1979).
A. Montanaro,On heat flux in simple media, J. Elasticity,30 (1993), pp. 81–101.
A. Montanaro,On the response functions of a thermo-elastic body, from the Mach-Painlevé point of view, Rend. Mat. Acc. Lincei, s. 9, v.1 (1990), pp. 3–29.
A. Montanaro,On tensor functions whose gradients have some skew-symmetries, Rend. Mat. Acc. Lincei, s. 9, v. 2 (1991), pp. 259–268.
A.Montanaro - D.Pigozzi,On the response functions for the heat flux in Differential bodies, to appear.
A.Montanaro - D.Pigozzi,On the physical indetermination of the response functions for general differential bodies. Part 1:Physical solutions of some symmetric systems of linear PDEs in tensor function. Part. 2:Some uniqueness and non uniqueness theorems on the response functions for the stress and internal energy in differential bodies, to appear.
C. Truesdell,A First Course in Rational Continuum Mechanics, Academic Press, London (1977).
Author information
Authors and Affiliations
Additional information
This work has been performed within the activity of the Consiglio Nazionale delle Ricerche, Group n. 3, in the academic years 1988/89 and 1989/90.
Rights and permissions
About this article
Cite this article
Montanaro, A., Pigozzi, D. On a large class of symmetric systems of linear PDEs, for tensor functions, useful in mathematical physics. Annali di Matematica pura ed applicata 164, 259–273 (1993). https://doi.org/10.1007/BF01759323
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01759323