耦合退化波动方程的精确能控性
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摘要
研究了耦合退化波动方程的精确能控性,应用乘子方法建立了相应的能观测性不等式,并用希尔伯特唯一性方法(HUM)证明了耦合退化波动方程的边界精确能控性。
Absrtact: The exact controllability of coupled degenerate wave equations were studied. The corresponding observability inequalities were established by multiplier method,and the boundary exact controllability of coupled degenerate wave equations were proved by Hilbert uniqueness method( HUM).
Absrtact: The exact controllability of coupled degenerate wave equations were studied. The corresponding observability inequalities were established by multiplier method,and the boundary exact controllability of coupled degenerate wave equations were proved by Hilbert uniqueness method( HUM).
引文
[1]BARBU V.Nonlinear differential equations of monotone types in Banach spaces[J].Springer monographs in mathematics,2010,24(3):25-32.
[2]BERTSCH M,GURTIN M E,HILHORST D.On a degenerate diffusion equation of the form c(z)t=φ(zx)xwith application to population dynamics[J].Journal differential equations,1987,67(1):56-89.
[3]CANNARSA P,MARTUNEZ P,VANCOSTENOBLE J.Persistent regional null controllability for a class of degenerate parabolic equations[J].Communications on pure and applied analysis,2004,3(4):607-635.
[4]CANNARSA P,MARTUNEZ P,VANCOSTENOBLE J.Carleman estimates and null controllability for boundary-degenerate parabolic operators[J].Comptes rendus-mathematique,2009,347(3/4):147-152.
[5]FATIHA A B,PIERMARCO C,GUNTER L.Control and stabilization of degenerate wave equations[J].Mathematics,2017,55(3):2052-2087.
[6]GUEYE M.Exact boundary controllability of 1-D parabolic and hyperbolic degenerate equations[J].SIAM journal on control and optimization,2014,52(4):2037-2054.
[7]BASTOS W D,SPEZAMIGLIO A,RAPOSO C A.On exact boundary controllability for linearly coupled wave equations[J].Journal mathematical analysis and application,2011,381(2):557-564.
[8]RAJARAM R,NAJAFI M.Exact controllability of wave equations in Rncoupled in parallel[J].Journal mathematical analysis and application,2009,356(1):7-12.
[9]AISSA G.Exact controllability for the wave equation with variable coefficients[J].Israel journal of mathematics,2001,125(1):83-92.
[10]ZHANG M M,GAO H.Null controllability of some degenerate wave equations[J].Journal of systems science and complexity,2017,30:1027-1041.
[11]GAO H,HOU X Z,PAVEL N H.Optional control and controllability problems for a class of nonlinear degenerate diffusion equations[J].Panamerican mathematical journal,2003,13(1):103-126.
[12]GUO L J,ZHANG J W,WANG Y Z.The exact controllability of wave equation with distuibance and damp terms[J].Journal of Taiyuan university of technology,2018,49(3):505-510.
[13]LEIVA H.Controllability of the strongly damped wave equation with impulses and delay[J].Nonautonomous dynamical systems,2017,4(1):31-39.
[14]SENGOUGA A.Observability and controllability of the 1-D wave in domains with moving boundary[J].Acta applicadae mathematicae,2018,157(1):117-128.
[15]LI T.Exact boundary observability for 1-D quasilinear wave equations[J].Mathematical methods in the applied sciences,2006,29(13):1543-1553.
[2]BERTSCH M,GURTIN M E,HILHORST D.On a degenerate diffusion equation of the form c(z)t=φ(zx)xwith application to population dynamics[J].Journal differential equations,1987,67(1):56-89.
[3]CANNARSA P,MARTUNEZ P,VANCOSTENOBLE J.Persistent regional null controllability for a class of degenerate parabolic equations[J].Communications on pure and applied analysis,2004,3(4):607-635.
[4]CANNARSA P,MARTUNEZ P,VANCOSTENOBLE J.Carleman estimates and null controllability for boundary-degenerate parabolic operators[J].Comptes rendus-mathematique,2009,347(3/4):147-152.
[5]FATIHA A B,PIERMARCO C,GUNTER L.Control and stabilization of degenerate wave equations[J].Mathematics,2017,55(3):2052-2087.
[6]GUEYE M.Exact boundary controllability of 1-D parabolic and hyperbolic degenerate equations[J].SIAM journal on control and optimization,2014,52(4):2037-2054.
[7]BASTOS W D,SPEZAMIGLIO A,RAPOSO C A.On exact boundary controllability for linearly coupled wave equations[J].Journal mathematical analysis and application,2011,381(2):557-564.
[8]RAJARAM R,NAJAFI M.Exact controllability of wave equations in Rncoupled in parallel[J].Journal mathematical analysis and application,2009,356(1):7-12.
[9]AISSA G.Exact controllability for the wave equation with variable coefficients[J].Israel journal of mathematics,2001,125(1):83-92.
[10]ZHANG M M,GAO H.Null controllability of some degenerate wave equations[J].Journal of systems science and complexity,2017,30:1027-1041.
[11]GAO H,HOU X Z,PAVEL N H.Optional control and controllability problems for a class of nonlinear degenerate diffusion equations[J].Panamerican mathematical journal,2003,13(1):103-126.
[12]GUO L J,ZHANG J W,WANG Y Z.The exact controllability of wave equation with distuibance and damp terms[J].Journal of Taiyuan university of technology,2018,49(3):505-510.
[13]LEIVA H.Controllability of the strongly damped wave equation with impulses and delay[J].Nonautonomous dynamical systems,2017,4(1):31-39.
[14]SENGOUGA A.Observability and controllability of the 1-D wave in domains with moving boundary[J].Acta applicadae mathematicae,2018,157(1):117-128.
[15]LI T.Exact boundary observability for 1-D quasilinear wave equations[J].Mathematical methods in the applied sciences,2006,29(13):1543-1553.