Blow up,Growth and Decay of Solutions for Class of a Coupled Nonlinear Viscoelastic Kirchhoff Equations with Variable Exponents and Fractional Boundary Conditions  

作　　者：Abdelbaki CHOUCHA Salah BOULAARAS Djamel OUCHENANE RashidJAN 

机构地区：[1]Department of Material Sciences,Faculty of Sciences,Amar Teleji Laghouat University,Algeria [2]Laboratory of Mathematics and Applied Sciences,Ghardaia University,Algeria [3]Department of Mathematics,College of Science,Qassim University,Buraydah,51452,Saudi Arabia [4]Department of Mathematics,Faculty of Sciences,Amar Teleji Laghouat University,Algeria [5]Institute of Energy Infrastructure(IEI),Department of Civil Engineering,College of Engineering,Universiti Tenaga Nasional(UNITEN),Putrajaya Campus,Jalan IKRAM-UNITEN,43000 Kajang,Selangor,Malaysia [6]Mathematics Research Center,Near East University TRNC,Mersin 10,Nicosia 99138,Turkey

出　　处：《Acta Mathematicae Applicatae Sinica》2025年第2期344-374,共31页应用数学学报(英文版)

摘　　要：We examine a quasilinear system of viscoelastic equations in this study that have fractional boundary conditions,dispersion,source,and variable-exponents.We discovered that the solution of the system is global and constrained under the right assumptions about the relaxation functions and initial conditions.After that,it is demonstrated that the blow-up has negative initial energy.Subsequently,the growth of solutions is demonstrated with positive initial energy,and the general decay result in the absence of the source term is achieved by using an integral inequality due to Komornik.

关 键 词：viscoelastic equation blow up nonlinear equations exponential growth general decay variable exponents 

分 类 号：O175.29[理学—数学]