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On the decay of solutions of a damped quasilinear wave equation with variable‐exponent nonlinearities
Author(s) -
Messaoudi Salim A.
Publication year - 2020
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.6254
Subject(s) - mathematics , bounded function , exponent , variable (mathematics) , domain (mathematical analysis) , mathematical analysis , wave equation , work (physics) , nonlinear system , range (aeronautics) , critical exponent , damped wave , physics , scaling , quantum mechanics , geometry , philosophy , linguistics , materials science , composite material
In this work, we consider the following nonlinear wave equation with variable exponents:u t t − d i v ( | ∇ u | r ( . ) − 2 ∇ u ) − Δ u t + | u t| m ( . ) − 2u t = 0 , in Ω × ( 0 , T ) , where Ω is a bounded domain, T > 0 , and m ( . ) and r ( . ) are continuous functions. We will establish several decay results depending on the range of the variable exponents m and r .