Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Exponential stability and global existence in thermoelasticity with radial symmetry


Author: Marc Oliver Rieger
Journal: Quart. Appl. Math. 62 (2004), 1-25
MSC: Primary 74H55; Secondary 35B35, 35Q72, 74D10, 74F05, 74H20
DOI: https://doi.org/10.1090/qam/2032570
MathSciNet review: MR2032570
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we consider equations of linear and nonlinear thermoelasticity with various boundary conditions. We assume radial symmetry of the initial data to prove exponential decay and to show the global existence of solutions of the nonlinear problem for small initial data.


References [Enhancements On Off] (What's this?)

  • [1] D. E. Carlson, Linear thermoelasticity, Handbuch der Physik VIa/2, Springer-Verlag, Berlin, 1972, 297-346
  • [2] W. Dan, On a Local in Time Solvability of the Neumann Problem of Quasilinear Hyperbolic Parabolic Coupled Systems, Math. Meth. Appl. Sci. 18, 1053-1082, 1995 MR 1357364
  • [3] S. Jiang, J. E. Muñoz Rivera, R. Racke, Asymptotic stability and global existence in thermoelasticity with symmetry, Quart. Appl. Math., LVI, 259, 1998 MR 1622566
  • [4] S. Jiang, R. Racke, Evolution Equations in Thermoelasticity, Chapman & Hall/CRC, 2000 MR 1774100
  • [5] H. Koch, Slow decay in linear thermoelasticity, Quart. Appl. Math. LVIII, no. 4, 601-612, 2000 MR 1788420
  • [6] R. Leis, Initial boundary value problems in mathematical physics, Teubner-Verlag, Stuttgart; John Wiley & Sons, Chichester et al., 1986 MR 841971
  • [7] S. Mizohata, The theory of partial differential equations, Cambridge Univ. Press, 1973 MR 0599580
  • [8] J.-L. Lions, Contrôlabilité exacte, perturbations et stabilisation de systémes distribués, tome 1, Masson, Paris, 1988 MR 953547
  • [9] R. Racke, Exponential Decay for a Class of Initial Boundary Value Problems in Thermoelasticity, Comp. Appl. Math. 12, 67-80, 1993 MR 1256166
  • [10] M. O. Rieger, Asymptotisches Verhalten radialsymmetrischer Lösungen von Thermoelastizitätsgleichungen (Asymptotic Behaviour of Radially Symmetric Solutions for Thermoelasticity Equations), diploma thesis, University of Konstanz, 1998
  • [11] J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer Verlag, New York et al., 1994 MR 1301779
  • [12] Y. Shibata, G. Nakamura, On a Local Existence Theorem of Neumann Problem for Some Quasilinear Hyperbolic Systems of 2nd Order, Mathematische Zeitschrift 202, 1-64, 1989 MR 1007739

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Additional Information

DOI: https://doi.org/10.1090/qam/2032570
Article copyright: © Copyright 2004 American Mathematical Society

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