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THEORETICAL AND NUMERICAL STUDY OF THE BLOW UP IN A NONLINEAR VISCOELASTIC PROBLEM WITH VARIABLE-EXPONENT AND ARBITRARY POSITIVE ENERGY
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作者 ala a.talahmeh Salim A.MESSAOUDI Mohamed alaHYANE 《Acta Mathematica Scientia》 SCIE CSCD 2022年第1期141-154,共14页
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
关键词 nonlinear damping blow up finite time variable nonlinearity arbitrary positive energy
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