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Existence and decay results for a von Karman equation with variable exponent nonlinearities
Author(s) -
Ha Tae Gab,
Park SunHye
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.7372
Subject(s) - mathematics , bounded function , exponent , mathematical analysis , variable (mathematics) , domain (mathematical analysis) , galerkin method , multiplier (economics) , stability (learning theory) , nonlinear system , physics , philosophy , linguistics , quantum mechanics , machine learning , economics , macroeconomics , computer science
In this article, we consider a von Karman equation with variable exponent nonlinearitiesw t t ( x , t ) +Δ 2 w ( x , t ) + | w t ( x , t ) | γ ( x ) − 2w t ( x , t ) = [ w ( x , t ) , F ( w ( x , t ) ) ] + | w ( x , t ) | p ( x ) − 2 w ( x , t ) in a bounded domain Ω ⊂ ℝ 2 . We firstly discuss an existence result of solutions by utilizing Faedo‐Galerkin approximation technique. Then, we undertake an investigation of asymptotic stability to the solutions by making use of the multiplier method.