In this paper,we consider the following nonlinear viscoelastic wave equation with variable exponents:utt-△u+∫_(0)^(t)g(t-τ)△u(x,τ)dτ+μut=|u|^(p(x)-2)-u,whereμis a nonnegative constant and the exponent of nonli...In this paper,we consider the following nonlinear viscoelastic wave equation with variable exponents:utt-△u+∫_(0)^(t)g(t-τ)△u(x,τ)dτ+μut=|u|^(p(x)-2)-u,whereμis a nonnegative constant and the exponent of nonlinearity p(·)and g are given functions.Under arbitrary positive initial energy and specific conditions on the relaxation function g,we prove a finite-time blow-up result.We also give some numerical applications to illustrate our theoretical results.展开更多
基金Birzeit UniversitySharjah University for their supportsponsored by MASEP Research Group in the Research Institute of Sciences and Engineering at University of Sharjah.Grant No.2002144089,2019-2020。
文摘In this paper,we consider the following nonlinear viscoelastic wave equation with variable exponents:utt-△u+∫_(0)^(t)g(t-τ)△u(x,τ)dτ+μut=|u|^(p(x)-2)-u,whereμis a nonnegative constant and the exponent of nonlinearity p(·)and g are given functions.Under arbitrary positive initial energy and specific conditions on the relaxation function g,we prove a finite-time blow-up result.We also give some numerical applications to illustrate our theoretical results.
