Title : ( BLOW-UP ANALYSIS FOR A CLASS OF PLATE VISCOELASTIC p(x)−KIRCHHOFF TYPE INVERSE SOURCE PROBLEM WITH VARIABLE-EXPONENT NONLINEARITIES )
Authors: Mohammad Shahrouzi , Jorge Ferreira , Erhan Piskin , Nouri Boumaza ,
Full TextAbstract
In this work, we study the blow-up analysis for a class of plate viscoelastic p(x)-Kirchho type inverse source problem of the form: utt + ∆2u − a + b ZΩ p(1x)jrujp(x)dx ∆p(x)u − Z0t g(t − τ)∆2u(τ)dτ + βjutjm(x)−2ut = αjujq(x)−2u + f(t)!(x): Under suitable conditions on kernel of the memory, initial data and variable exponents, we prove the blow up of solutions in two cases: linear damping term (m(x) ≡ 2) and nonlinear damping term (m(x) > 2). Precisely, we show that the solutions with positive initial energy blow up in a nite time when m(x) ≡ 2 and blow up at innity if m(x) > 2.
Keywords
, inverse source problem, blow-up, viscoelastic, p(x)-Kirchhoff type equation.
@article{paperid:1104640,
author = {Shahrouzi, Mohammad and Jorge Ferreira and Erhan Piskin and Nouri Boumaza},
title = {BLOW-UP ANALYSIS FOR A CLASS OF PLATE VISCOELASTIC p(x)−KIRCHHOFF TYPE INVERSE SOURCE PROBLEM WITH VARIABLE-EXPONENT NONLINEARITIES},
journal = {Siberian Electronic Mathematical Reports},
year = {2022},
volume = {19},
number = {2},
month = {October},
issn = {1813-3304},
pages = {912--934},
numpages = {22},
keywords = {inverse source problem; blow-up; viscoelastic; p(x)-Kirchhoff type equation.},
}
%0 Journal Article
%T BLOW-UP ANALYSIS FOR A CLASS OF PLATE VISCOELASTIC p(x)−KIRCHHOFF TYPE INVERSE SOURCE PROBLEM WITH VARIABLE-EXPONENT NONLINEARITIES
%A Shahrouzi, Mohammad
%A Jorge Ferreira
%A Erhan Piskin
%A Nouri Boumaza
%J Siberian Electronic Mathematical Reports
%@ 1813-3304
%D 2022
