Existence and exponential decay for contact problems in thermoelasiticity

References

• Andrews , K. T. , Shi , P. , Shillor , M. and Wright , S. 1993 . Thermoelastic contact with Barber's heat exchange condition . Appl. Math. Opt , 28 ( 1 ) : 11 – 48 .
   Web of Science ®Google Scholar
• Carlson , D.E. 1972 . Linear thermoelasticity, in Handbuch der physik Edited by: Truesdell , C. Vol. VIa/2 ,
   Google Scholar
• Chiriţã , S. 1987 . On the asymptotic partition of the energy in linear thermoelasticity . Quaterly of App. Math , XLV ( 2 ) : 327 – 370 .
   Web of Science ®Google Scholar
• Copetti , MIM and Elliot , C. M. 1993 . A one dimensional quasi-static contact problem in linear thermoelasticity . Eur. J. Appl. Math , 4 ( 2 ) : 151 – 174 .
   Google Scholar
• Dafermos , C. M. 1968 . On the existence and the asymptotic stability of solutions to the equation of linear thermoelasticity . Arch. Rat. Mech. Anal , 29 ( 2 ) : 241 – 271 .
   Web of Science ®Google Scholar
• Dassios , G. and Grillakis , M. 1984 . Dissipation rates and partition of energy in thermoelasticity . Arch. Rat. Mech. Anal , 87 ( 1 ) : 49 – 91 .
   Web of Science ®Google Scholar
• Day , W. A. 1986 . Heat conduction within Linear thermoelasticity , Oxford : Pergamon .
   Google Scholar
• Elliot , C. M. and Qi , T. 1994 . A dynamic contact problem in thermoelasticity . Nonlinear Analisys , 23 ( 7 ) : 883 – 898 .
   Web of Science ®Google Scholar
• Gilbert , R. P. , Shi , P. and Shillor , M. 1990 . A quasistatic contact problem in linear thermoelasticity . Rendiconti di Mat , 10 : 785 – 808 .
   Google Scholar
• Hansen , S. W. 1992 . Exponential energy decay on a thermoelastic rod . Journal of Math. Analysis and Application , 167 ( 2 ) : 429 – 442 .
   Web of Science ®Google Scholar
• Henry , D.B. , Perissinitto , A. Jr. and Lopes , O. 1993 . Asymptotic behaviour of a semigroup of the thermoelasticity . J. Nonlinear Analysis , 21 ( 1 ) : 65 – 75 .
   Web of Science ®Google Scholar
• Kim , J.U. 1992 . On the energy decay of a linear thermoelastic bar and plate . SIAM J. Math. Anal , 23 ( 1 ) : 889 – 899 .
   Google Scholar
• Kim , J. U. 1989 . A boundary thin obstacle problem for a wave equation . Comm. Partial Diff. Equations , 14 ( 8&9 ) : 1011 – 1026 .
   Web of Science ®Google Scholar
• Jiang , S. , Muñoz Rivera , J. E. and Racke , R. 1998 . Asymptptoc stability and global existence in thermoelasticity with symmetry . Quarterly of applied Math , LVI ( 2 ) : 259 – 276 .
   Web of Science ®Google Scholar
• Kawashima , S. and Shibata , Y. 1992 . On the Neumann problem of the one-dimensional nonlinear thermoelasticity with time-independent external forces . Czechoslovak Math. Journal , LVI ( 2 ) : 1 – 31 .
   Google Scholar
• Muñoz rivera , J. E. 1992 . Energy decay rates in linear thermoelasticity . Funkcialaj Etvacioj , 35 ( 1 ) : 19 – 30 .
   Google Scholar
• Muñoz Rivera , J.E. 1993 . Decomposition of the displacement vector field and decay rates in linear thermoelasticity . SIAM J. Math. Anal , 24 ( 2 ) : 390 – 406 .
   Web of Science ®Google Scholar
• Renardy , M. 1993 . On the type of certain C 0-semigroups . Communication in Partial Differential Equation , 18 ( 2 ) : 1299 – 1307 .
   Web of Science ®Google Scholar
• Shi , P. and Shillor , M. 1990 . Uniqueness and stability of the solution to a thermoelastic contact problem . Euro. J. Appl. Math , 1 ( 2 ) : 371 – 387 .
   Google Scholar
• Shi , P. and Shillor , M. 1993 . A quasistatic contact problem in thermoelasticity with a radiation condition for the temperature . J. Math. Anal. Appl , 172 ( 1 ) : 147 – 165 .
   Web of Science ®Google Scholar
• Shi , P. , Shillor , M. and Zou , X. L. 1991 . Numerical solution to the one dimensional problems of thermoelastic contact . Comput. Math. Appl , 22 ( 10 ) : 65 – 78 .
   Web of Science ®Google Scholar