第三型热弹Timoshenko型方程组指数衰减（英文）
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摘要
In this work, a Timoshenko system of type Ⅲ of thermoelasticity with frictional versus viscoelastic under Dirichlet-Dirichlet-Neumann boundary conditions was considered.By exploiting energy method to produce a suitable Lyapunov functional, we establish the global existence and exponential decay of type-Ⅲ case.
In this work, a Timoshenko system of type Ⅲ of thermoelasticity with frictional versus viscoelastic under Dirichlet-Dirichlet-Neumann boundary conditions was considered.By exploiting energy method to produce a suitable Lyapunov functional, we establish the global existence and exponential decay of type-Ⅲ case.
In this work, a Timoshenko system of type Ⅲ of thermoelasticity with frictional versus viscoelastic under Dirichlet-Dirichlet-Neumann boundary conditions was considered.By exploiting energy method to produce a suitable Lyapunov functional, we establish the global existence and exponential decay of type-Ⅲ case.
引文
[1]TIMOSHENKO S.On the correction for shear of the differential equation for transverse vibrations of prismaticbars[J].Philisophical Magazine,1921,41:744-746.
[2]KIM J U,RENARDY Y.Boundary control of the Timoshenko beam[J].SIAM J Control Optim,1987,25:1417-1429.
[3]RAPOSO CA,FERREIRA J,SANTOS ML,CASTRO NNO.Exponential stability for the Timoshenko system with two week dampings[J].Applied Mathematics Letters,2005,18:535-541.
[4]SOUFYANE A,WEHBE A.Uniform stabilization for the Timoshenko beam by a locally distributed damping[J].Electronic Jounrnal of Differential Equations,2003,29:1-14.
[5]AMAR-KHODJA F,BENABADALAH A.Mu?oz River J.E.and Racke R.,Energy decay for Timoshenko systems of memory type[J].J Diff Equations,2003,194:82-115.
[6]MU?OZ RIVER J E,RACKE R.Mildly disspative nonlinear Timoshenko systems global exsitence and exponential stability[J].J math Anal Appl,2001,276:248-278.
[7]MESSAOUDI SA,POCOJOVY M,SAID-HOUARRI B.Nonlinear damped Timoshenko systems with second sound-global existence and exponential stability[J].Math Meth Appl Sci,2009,32:505-534.
[8]GUESMIA A,MESSAOUDI S A.General enerhy decay estimate of Timoshenko system with frictional versus viscoelastic damping[J].Math Meth Appl Sci,2009,32:2102-2122.
[9]OOUCHENANE D,REHMOUNE A.General decay result of the Timoshenko system in thermoelasticty of second sound[J].elextronic Journal od Mathematical Analysis and Applications,2018,6:45-64.
[10]ZHENG S.Nonlinear evolution equations[M].Monographs and Surveys in Pure and Applied Mathematics,2004,133.
[11]RIVERA,MU?0Z.Teoria das Distribuic?es e Equac?es Diferenciais Parciais[J].Textos Avanzados-LNCC,1999.
[12]ROBERT A,ADAMS,JOHN J F.Fournier,Sobolev Space[M].Elsevier Pte Ltd,2003.
[13]K M,MESSAOUDI S A,S A.Well-posedness and stability results in a Timoshenko-type system of thermolasticty of type Ⅲ with delay[J].Z Angew Math Phys,2015,65:1499-1517.
[14]JIANG H,JING W.Global existence and stability results for a nonlinear Timoshenko system of thermolasticty of type Ⅲ with delay[J].Boundary Value Problems,2018,65.
[15]MESSAOUDI A,FAREH A.Energy decay in a Timoshenko-type system of thermoelasticity of type Ⅲ with different wave-propagation speeds[J].Ara J Math,2013,2:199-207.
[16]GUESMIA A.Some well-posedness and general stability results in Timoshenko system with infinite memory and distributed time delay[J].Journal of Mathematical Physics,2014,55.
[17]FAREH A,MESSAOUDI S A.Stabilization of a type Ⅲ thermoelastic Timoshenko system in the presence of a time-distributed delay[J].Math Narchr,2017,290:1017-1032.
[18]MESSAOUDI S A,SAID-HOUARI B.Energy decay in a timoshenko-type system of thermoelasticity of type Ⅲ[J].Journal Math Anal Appl,2008,348:298-307.
[19]KAFINI M.Genaral energy decay in a Timoshenko-type system of thermoelasticity of type Ⅲ with a viscoelastic damping[J].Journal Math Anal Appl,2011,375:523-537.
[20]QIN Y.Nonlinear Parabolic-Hyperbolic Coupled Systems and Their Attractors[M].Volume 184,Advances in Partial Differential Equations,Birkhauser Verlag AG,Basel-Boston-Berlin,2008.
[21]QIN Y,FENG B,ZHANG M.Large-time behavior of solutions for the one-dimensional infrarelativistic model of a compressible viscous gas with radiation[J].J Differential Equations,2012,252:6175-6213.
[22]QIN Y,FENG B,ZHANG M.Large-time behavior of solutions for the 1D viscous heat-conducting gas with radiation:the pure scattering case[J].J Differential Equations,2014,256:989-1042.
[23]QIN Y,HUANG L.On the 1D viscous reactive and radiative gas with the one-order Arrhenius kinetics[M].Preprint.
[24]QIN Y,HUANG L.Global well-Posedness of Nonlinear Parabolic-Hyperbolic Coupled Systems[J].Frontiers in Mathematics,Springer Basel AG,2012.
[2]KIM J U,RENARDY Y.Boundary control of the Timoshenko beam[J].SIAM J Control Optim,1987,25:1417-1429.
[3]RAPOSO CA,FERREIRA J,SANTOS ML,CASTRO NNO.Exponential stability for the Timoshenko system with two week dampings[J].Applied Mathematics Letters,2005,18:535-541.
[4]SOUFYANE A,WEHBE A.Uniform stabilization for the Timoshenko beam by a locally distributed damping[J].Electronic Jounrnal of Differential Equations,2003,29:1-14.
[5]AMAR-KHODJA F,BENABADALAH A.Mu?oz River J.E.and Racke R.,Energy decay for Timoshenko systems of memory type[J].J Diff Equations,2003,194:82-115.
[6]MU?OZ RIVER J E,RACKE R.Mildly disspative nonlinear Timoshenko systems global exsitence and exponential stability[J].J math Anal Appl,2001,276:248-278.
[7]MESSAOUDI SA,POCOJOVY M,SAID-HOUARRI B.Nonlinear damped Timoshenko systems with second sound-global existence and exponential stability[J].Math Meth Appl Sci,2009,32:505-534.
[8]GUESMIA A,MESSAOUDI S A.General enerhy decay estimate of Timoshenko system with frictional versus viscoelastic damping[J].Math Meth Appl Sci,2009,32:2102-2122.
[9]OOUCHENANE D,REHMOUNE A.General decay result of the Timoshenko system in thermoelasticty of second sound[J].elextronic Journal od Mathematical Analysis and Applications,2018,6:45-64.
[10]ZHENG S.Nonlinear evolution equations[M].Monographs and Surveys in Pure and Applied Mathematics,2004,133.
[11]RIVERA,MU?0Z.Teoria das Distribuic?es e Equac?es Diferenciais Parciais[J].Textos Avanzados-LNCC,1999.
[12]ROBERT A,ADAMS,JOHN J F.Fournier,Sobolev Space[M].Elsevier Pte Ltd,2003.
[13]K M,MESSAOUDI S A,S A.Well-posedness and stability results in a Timoshenko-type system of thermolasticty of type Ⅲ with delay[J].Z Angew Math Phys,2015,65:1499-1517.
[14]JIANG H,JING W.Global existence and stability results for a nonlinear Timoshenko system of thermolasticty of type Ⅲ with delay[J].Boundary Value Problems,2018,65.
[15]MESSAOUDI A,FAREH A.Energy decay in a Timoshenko-type system of thermoelasticity of type Ⅲ with different wave-propagation speeds[J].Ara J Math,2013,2:199-207.
[16]GUESMIA A.Some well-posedness and general stability results in Timoshenko system with infinite memory and distributed time delay[J].Journal of Mathematical Physics,2014,55.
[17]FAREH A,MESSAOUDI S A.Stabilization of a type Ⅲ thermoelastic Timoshenko system in the presence of a time-distributed delay[J].Math Narchr,2017,290:1017-1032.
[18]MESSAOUDI S A,SAID-HOUARI B.Energy decay in a timoshenko-type system of thermoelasticity of type Ⅲ[J].Journal Math Anal Appl,2008,348:298-307.
[19]KAFINI M.Genaral energy decay in a Timoshenko-type system of thermoelasticity of type Ⅲ with a viscoelastic damping[J].Journal Math Anal Appl,2011,375:523-537.
[20]QIN Y.Nonlinear Parabolic-Hyperbolic Coupled Systems and Their Attractors[M].Volume 184,Advances in Partial Differential Equations,Birkhauser Verlag AG,Basel-Boston-Berlin,2008.
[21]QIN Y,FENG B,ZHANG M.Large-time behavior of solutions for the one-dimensional infrarelativistic model of a compressible viscous gas with radiation[J].J Differential Equations,2012,252:6175-6213.
[22]QIN Y,FENG B,ZHANG M.Large-time behavior of solutions for the 1D viscous heat-conducting gas with radiation:the pure scattering case[J].J Differential Equations,2014,256:989-1042.
[23]QIN Y,HUANG L.On the 1D viscous reactive and radiative gas with the one-order Arrhenius kinetics[M].Preprint.
[24]QIN Y,HUANG L.Global well-Posedness of Nonlinear Parabolic-Hyperbolic Coupled Systems[J].Frontiers in Mathematics,Springer Basel AG,2012.