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Global and blow‐up of solutions for a quasilinear parabolic system with viscoelastic and source terms
Author(s) -
Liu Gongwei,
Chen Hua
Publication year - 2013
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.2792
Subject(s) - mathematics , bounded function , viscoelasticity , work (physics) , mathematical analysis , differentiable function , function (biology) , boundary value problem , energy (signal processing) , energy method , matrix (chemical analysis) , initial value problem , positive definite matrix , boundary (topology) , physics , thermodynamics , eigenvalues and eigenvectors , statistics , materials science , quantum mechanics , evolutionary biology , biology , composite material
In this work, we consider an initial boundary value problem related to the quasilinear parabolic equation A ( t ) | u t| m − 2u t − △ u + ∫ 0 t g ( t − s ) △ u ( x , s ) d s = | u | p − 2 u , for m ≥ 2, p ≥ 2, A ( t ) a bounded and positive definite matrix, and g a continuously differentiable decaying function, and prove, under suitable conditions on g and p , a general decay of the energy function for the global solution and a blow‐up result for the solution with both positive and negative initial energy. Copyright © 2013 John Wiley & Sons, Ltd.