A renorming method for thermoelastic models

References

• Avalos , G. and Lasiecka , I. 1998 . Exponential stability of a thermoelastic system with free boundary conditions without mechanical dissipation . Siam J. Math. Anal , 29 : 155 – 182 .
   Web of Science ®Google Scholar
• Banks , H. T. , Ito , K. and Wang , C. 1991 . “ Exponentially stable approximations of weakly damped wave equations ” . In In International Series in Numerical Mathematics , Vol. 100 , 1 – 33 . Birkhäuser .
   Google Scholar
• Burns , J. A. , Liu , Z. and Miller , R. E. 1991 . Approximations of thermoelastic and viscoelastic control systems . Numer. Functional Anal. Optim , 12 : 79 – 136 .
   Google Scholar
• Burns , J. A. , Liu , Z. and Zheng , S. 1993 . On the energy decay of a linear thermoelastic bar . J. Math. Anal. Appl , 179 : 574 – 591 .
   Web of Science ®Google Scholar
• Day , A. 1985 . Heat Conduction Within Linear Thermoelasticity , Springer— Verlag .
   Google Scholar
• Driscoll , T. A. and Trefethen , L. N. 1996 . Pseudospectra for the wave equation with an absorbing boundary . J. Comp. and Applied Math , 69 : 125 – 142 .
   Google Scholar
• Fabiano R. H. Renorming for stability and approximation of linear systems: Examples. Mathematical and Computer Modeling to appear
   Google Scholar
• Fabiano , R. H. 1995 . Preserving exponential stability under approximation for distributed parameter systems , Edited by: Bowers , K. and Lund , J. 143 – 154 . Birkhäuser . Computation and Control IV, Progress in Systems and Control Theory
   Google Scholar
• Fabiano , R. H. 1995 . Stability preserving spline approximations for scalar functional differential equations . Computers Math. Applic , 29 ( 8 ) : 87 – 94 .
   Web of Science ®Google Scholar
• Fabiano , R. H. 1996 . Stability and approximation for a linear viscoelastic model . Journal of Mathematical Analysis and Applications , 204 ( 8 ) : 206 – 220 .
   Google Scholar
• Fabiano , R. H. 1999 . Coercive forms associated with elastic systems with damping . J. Comput. and Appl. Math , 114 ( 8 ) : 159 – 171 .
   Google Scholar
• Fabiano , R. H. and Turi , J. 1999 . Preservation of stability under approximation for a neutral FDE . Dynamics of Continuous, Discrete and Impulsive Systems , 5 ( 8 ) : 351 – 364 .
   Google Scholar
• Gibson , J. S. , Rosen , I. G. and Tao , G. 1992 . Approximation in control of thermoelastic systems . Siam J. Control Optim , 30 ( 8 ) : 1163 – 1189 .
   Google Scholar
• Hansen , S. W. 1992 . Exponential energy decay in a linear thermoelastic rod . J. Math. Anal. Appl , 167 ( 8 ) : 429 – 442 .
   Google Scholar
• Kappel , F. and Salamon , D. 1989 . On the stability properties of spline approximations for retarded systems . Siam. J. Control and Optimization , 27 ( 8 ) : 407 – 431 .
   Google Scholar
• Kim , J. U. 1992 . On the energy decay of a linear thermoelastic bar and plate . Siam J. Math. Anal , 23 ( 8 ) : 889 – 899 .
   Google Scholar
• Liu , K. and Liu , Z. 1997 . Exponential stability and analyticity of abstract linear thermoelastic systems . Z. angew. Math. Phys , 48 ( 8 ) : 885 – 904 .
   Google Scholar
• Liu , Z. and Renardy , M. 1995 . A note on the equations of a thermoelastic plate . Appl. Math. Letters , 8 ( 8 ) : 1 – 6 .
   Google Scholar
• Liu , Z. and Zheng , S. 1993 . Exponential stability of the semigroup associated with a thermoelastic system . Quarterly of Applied Mathematics , 51 ( 8 ) : 535 – 545 .
   Google Scholar
• Liu , Z. and Zheng , S. 1994 . Uniform exponential stability and approximation in control of a thermoelastic system . Siam J. Control Opt , 32 ( 8 ) : 1226 – 1246 .
   Google Scholar
• Pazy , A. 1983 . Semigroups of Linear Operators and Applications to Partial Differential Equations , Vol. 44 , Springer—Verlag . Applied Mathematical Sciences
   Google Scholar
• Racke , R. 1996 . “ Nonlinear evolution equations in thermoelasticity ” . In Institute of Mathematics , University of Tsukuba . Math. Research Note 96-004
   Google Scholar
• Rivera , J. E. M. and Racke , R. 1995 . Smoothing properties, decay and global existence of solutions to nonlinear coupled systems of thermoelastic type . Siam J. Math. Anal , 26 : 1547 – 1563 .
   Web of Science ®Google Scholar
• Russell , D. L. 1993 . A general framework for the study of indirect damping mechanisms in elastic systems . J. Math. Anal. Appl , 173 : 339 – 358 .
   Web of Science ®Google Scholar
• Showalter , R. E. 1977 . Hilbert Space Methods for Partial Differential Equations , Pitman .
   Google Scholar
• Tanabe , H. 1979 . Equations of Evolution , Pitman .
   Google Scholar
• Trefethen , L. N. 1997 . Siam Review , 39 : 383 – 406 .
   Web of Science ®Google Scholar
• Wloka , J. 1987 . Partial Differential Equations , Cambridge University Press .
   Google Scholar