Energy estimates to the Cauchy problem of a weakly damped Klein‐Gordon equation with variable‐exponent nonlinearity | Zendy

Mustafa Muhammad I. | Zendy

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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 .

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