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Finite time blow‐up and stability properties of materials with fading memory
Author(s) -
Calderer M. C.,
Hsiao G.
Publication year - 1987
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670090103
Subject(s) - mathematics , dissipation , nonlinear system , boundary value problem , elasticity (physics) , mathematical analysis , partial differential equation , stability (learning theory) , physics , thermodynamics , computer science , quantum mechanics , machine learning
A detailed analysis of the equations of nonlinear elasticity is carried out for a certain class of initial‐boundary value problems. In particular, I examine whether the presence in the differential equation of a mechanical mechanism of dissipation is able to prevent instabilities and ensure global existence in time of the solutions.