General and physically privileged solutions to certain symmetric systems of linear P.D.E.s with tensor functionals as unknowns

Montanaro, Adriano, and Pigozzi, Diego. "General and physically privileged solutions to certain symmetric systems of linear P.D.E.s with tensor functionals as unknowns." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 11.4 (2000): 245-276. <http://eudml.org/doc/252306>.

@article{Montanaro2000,
abstract = {We characterize the general solutions to certain symmetric systems of linear partial differential equations with tensor functionals as unknowns. Then we determine the solutions that are physically meaningful in suitable senses related with the constitutive functionals of two simple thermodynamic bodies with fading memory that are globally equivalent, i.e. roughly speaking that behave in the same way along processes not involving cuts. The domains of the constitutive functionals are nowhere dense subsets of a suitable infinite-dimensional Hilbert space. By using the condition of material frame-indifference on the constitutive functionals and the theory [1] of differential calculus on convex sets (that may be nowhere dense), we give a rigorous meaning from a general point of view to the derivatives of these functionals, without assuming the possibility of extending them to an open set. Such results appear necessary for characterizing the couples of thermodynamic bodies with memory that are globally equivalent but are physically different; and such bodies exist.},
author = {Montanaro, Adriano, Pigozzi, Diego},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Linear partial differential equations; Tensor functionals; Symmetric linear systems; symmetric partial differential equations; tensor functionals; continuum thermodynamics; linear systems; second-order tensors; physically consistent solutions; convex nowhere dense sets; fading-memory bodies},
language = {eng},
month = {12},
number = {4},
pages = {245-276},
publisher = {Accademia Nazionale dei Lincei},
title = {General and physically privileged solutions to certain symmetric systems of linear P.D.E.s with tensor functionals as unknowns},
url = {http://eudml.org/doc/252306},
volume = {11},
year = {2000},
}

TY - JOUR
AU - Montanaro, Adriano
AU - Pigozzi, Diego
TI - General and physically privileged solutions to certain symmetric systems of linear P.D.E.s with tensor functionals as unknowns
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2000/12//
PB - Accademia Nazionale dei Lincei
VL - 11
IS - 4
SP - 245
EP - 276
AB - We characterize the general solutions to certain symmetric systems of linear partial differential equations with tensor functionals as unknowns. Then we determine the solutions that are physically meaningful in suitable senses related with the constitutive functionals of two simple thermodynamic bodies with fading memory that are globally equivalent, i.e. roughly speaking that behave in the same way along processes not involving cuts. The domains of the constitutive functionals are nowhere dense subsets of a suitable infinite-dimensional Hilbert space. By using the condition of material frame-indifference on the constitutive functionals and the theory [1] of differential calculus on convex sets (that may be nowhere dense), we give a rigorous meaning from a general point of view to the derivatives of these functionals, without assuming the possibility of extending them to an open set. Such results appear necessary for characterizing the couples of thermodynamic bodies with memory that are globally equivalent but are physically different; and such bodies exist.
LA - eng
KW - Linear partial differential equations; Tensor functionals; Symmetric linear systems; symmetric partial differential equations; tensor functionals; continuum thermodynamics; linear systems; second-order tensors; physically consistent solutions; convex nowhere dense sets; fading-memory bodies
UR - http://eudml.org/doc/252306
ER -