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A 3D‐2D asymptotic analysis of viscoelastic problem with nonlinear dissipative and source terms
Author(s) -
Dilmi Mohamed,
Dilmi Mourad,
Benseridi Hamid
Publication year - 2019
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.5755
Subject(s) - mathematics , dissipative system , uniqueness , viscoelasticity , mathematical analysis , limit (mathematics) , asymptotic analysis , nonlinear system , domain (mathematical analysis) , uniqueness theorem for poisson's equation , physics , quantum mechanics , thermodynamics
The purpose of this article is to study the asymptotic analysis of the solutions of a linear viscoelastic problem with a dissipative and source terms in a three‐dimensional thin domain Ω ε . Firstly, we give the strong formulation of the problem and the existence and uniqueness theorem of the weak solution. Then, we establish some estimates independent of the parameter ε . These last will be useful to obtain the limit problem with a specific weak form of the Reynolds equation.