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Continuous dependence and uniqueness theorems in boundary‐initial value problems for a class of porous bodies occupying bounded or unbounded domains
Author(s) -
Borrelli Alessandra,
Patria Maria Cristina
Publication year - 1984
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300012420
Subject(s) - mathematics , uniqueness , bounded function , inviscid flow , domain (mathematical analysis) , sign (mathematics) , mathematical analysis , class (philosophy) , boundary value problem , constant (computer programming) , infinity , boundary (topology) , zero (linguistics) , uniqueness theorem for poisson's equation , pure mathematics , classical mechanics , linguistics , philosophy , artificial intelligence , computer science , physics , programming language
Summary In this paper the authors formulate a boundary‐initial value problem for a linear elastic porous body saturated with an inviscid fluid and establish a continuous dependence theorem (Theorem 2) and two uniqueness theorems (Theorems 3, 4) for a particular class of such continua. Theorems 2, 3 are proved without hypotheses on the sign of the constants and, if the domain is unbounded, under mild assumptions on the spatial asymptotic behaviour of the field variables. Theorem 4 holds for body‐forces not equal to zero and, if the domain is unbounded, without restrictions upon the behaviour of the unknown fields at infinity, but under suitable conditions on the sign of the constants.