一类具有记忆项的耦合方程组的全局吸引子
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摘要
本文研究一类具有记忆项的耦合方程组的全局吸引子的问题.利用Faedo-Galerkin方法,获得方程的解的存在性,通过证明系统吸收集的存在性和半群S(t)的渐近紧性,进而证明方程组的全局吸引子的存在性.
In this paper, we study the problem of global attractors for a class of coupled equations with memory term. By using Faedo-Galerkin method, we obtain the existence of the solutions of the equations. By proving the existence of the system absorption set and the asymptotic compactness of the semigroup of S(T),we further prove the existence of the global attractor for the equations.
In this paper, we study the problem of global attractors for a class of coupled equations with memory term. By using Faedo-Galerkin method, we obtain the existence of the solutions of the equations. By proving the existence of the system absorption set and the asymptotic compactness of the semigroup of S(T),we further prove the existence of the global attractor for the equations.
引文
[1]KIRCHHOFF G.Vorlessunger Uber Mathematiche Physik[M].Teubner,Leipzig:Mechanik,1876.
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[7]NAKAO M.Global attractors for wave equations with nonlinear dissipative terms[J].Differential Equations,2006,227(1):204-229.
[8]CHUESHOV I,LASIECKA I.Long-time behavior of second order evolution equations with nonlinear damping[J].Memoirs of the American Mathematical Society,2008,195:67-99.
[9]KANG Jumran.Long-time behavior of a suspension bridge equations with past history[J].Applied Mathematics and Computation,2015,265:509-519.
[10]BARBOSA A R A,MA T F.Long-time dynamics of an extensible plate equation with thermal memory[J].Math.Anal.Appl.,2014,416(1):143-165.
[11]NARCISO V.Long-time behavior of a nonlinear viscoelastic beam equation with past history[J].Math.Meth.Appl.Sci.,2015,38(4):775-784.
[2]PARK J Y,KANG J R.Global attractor for hyperbolic equation with nonlinear damping and linear memory[J].Sci.China Math.,2010,53(6):1531-1539.
[3]EDEN A,MILANI A J.Exponential attractor for extensible beam equations[J].Nonlinearity.,1993,6:457-479.
[4]MA T F,NARCISO V,PELICER M L.Pelicer,Long-time behavior of a model of extensible beams with nonlinear boundary dissipations[J].Math.Anal.Appl.,2012,396(2):694-703.
[5]CAVALCANTI M M,DOMINGOS N,SORIANO J A.Global existence and asymptotic stability for the nonlinear and generalized damped extensible plate equation[J].Communications Contemporary Mathematics,2004,6(5):705-731.
[6]BALL J M.Stability theory for an extensible beam[J].Differ.Equ.,1973,14:399-418.
[7]NAKAO M.Global attractors for wave equations with nonlinear dissipative terms[J].Differential Equations,2006,227(1):204-229.
[8]CHUESHOV I,LASIECKA I.Long-time behavior of second order evolution equations with nonlinear damping[J].Memoirs of the American Mathematical Society,2008,195:67-99.
[9]KANG Jumran.Long-time behavior of a suspension bridge equations with past history[J].Applied Mathematics and Computation,2015,265:509-519.
[10]BARBOSA A R A,MA T F.Long-time dynamics of an extensible plate equation with thermal memory[J].Math.Anal.Appl.,2014,416(1):143-165.
[11]NARCISO V.Long-time behavior of a nonlinear viscoelastic beam equation with past history[J].Math.Meth.Appl.Sci.,2015,38(4):775-784.