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Energy estimates to the Cauchy problem of a weakly damped Klein‐Gordon equation with variable‐exponent nonlinearity
Author(s) -
Mustafa Muhammad I.
Publication year - 2021
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.7327
Subject(s) - mathematics , klein–gordon equation , exponent , nonlinear system , mathematical analysis , multiplier (economics) , variable coefficient , cauchy problem , mathematical physics , initial value problem , variable (mathematics) , energy (signal processing) , physics , quantum mechanics , statistics , philosophy , linguistics , economics , macroeconomics
In we consider the following Klein‐Gordon equationu t t − Δ u + u + α ( t )u tm ( · ) − 2u t = 0 inR n × (0, T ) with a nonlinear feedback having a variable exponent m ( x ) and a time‐dependent coefficient α ( t ). We use the multiplier method to establish energy decay results depending on both m and α .