General and physically privileged solutions to certain symmetric systems of linear PDE's with tensor functionals as unknowns
type: Item
instance of: scholarly article
title: General and physically privileged solutions to certain symmetric systems of linear PDE's with tensor functionals as unknowns
zbMATH Open document ID: 1020.74003
author: Diego Pigozzi
author: A. Montanaro
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2003-03-18T00:00:00Z
review text: This paper develops a rather thorough study of linear systems of symmetric partial differential equations that model, under continuum thermodynamic hypotheses, the macroscopic behavior of physical bodies. Such equations carry, as unknown, functionals with values in the space of second-order tensors in three-dimensional Euclidean space. The set of general solutions for the considered equations is characterized. Further, a subset of physically consistent solutions is described. It is worth emphasizing the use of differential tools for functionals defined on convex nowhere dense sets, but without requiring their extension to open sets. The need of such a methodology is pointed out: mainly, it is required when one needs to consider fading-memory bodies that are physically distinct but globally equivalent, i.e. that exhibit the same behavior when the same thermodynamic conditions are imposed.
Mathematics Subject Classification ID: 74A15
Mathematics Subject Classification ID: 80A17
Mathematics Subject Classification ID: 35Q72
zbMATH DE Number: 1884303
zbMATH Keywords: symmetric partial differential equations
zbMATH Keywords: tensor functionals
zbMATH Keywords: continuum thermodynamics
zbMATH Keywords: linear systems
zbMATH Keywords: second-order tensors
zbMATH Keywords: physically consistent solutions
zbMATH Keywords: convex nowhere dense sets
zbMATH Keywords: fading-memory bodies
MaRDI profile type: Publication
Recommended article: On a large class of symmetric systems of linear PDEs, for tensor functions, useful in mathematical physics
Recommended article: Generalized symmetries of partial differential equations and quasi-exact solvability
Recommended article: On the solutions of a class of tensor equations
Recommended article: Q5844052
Recommended article: Q3086550
Recommended article: Solutions to nonlinear partial differential equations from symmetry-enhancing and symmetry-preserving constraints
Recommended article: Symmetries of linear partial differential equations and fundamental solutions
Recommended article: Tensor methods for solving symmetric \({\mathcal {M}}\)-tensor systems
Recommended article: Symmetry and monotonicity of positive solutions to systems involving general pseudo-relativistic operators
Recommended article: Q4722481
description: scientific article; zbMATH DE number 1884303