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
Full-text PDF Free Access
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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.
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D. E. Carlson, Linear thermoelasticity, Handbuch der Physik VIa/2, Springer-Verlag, Berlin, 1972, 297–346
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
S. Jiang, J. E. Muñoz Rivera, R. Racke, Asymptotic stability and global existence in thermoelasticity with symmetry, Quart. Appl. Math., LVI, 259, 1998
S. Jiang, R. Racke, Evolution Equations in Thermoelasticity, Chapman & Hall/CRC, 2000
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S. Mizohata, The theory of partial differential equations, Cambridge Univ. Press, 1973
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R. Racke, Exponential Decay for a Class of Initial Boundary Value Problems in Thermoelasticity, Comp. Appl. Math. 12, 67–80, 1993
M. O. Rieger, Asymptotisches Verhalten radialsymmetrischer Lösungen von Thermoelastizitätsgleichungen (Asymptotic Behaviour of Radially Symmetric Solutions for Thermoelasticity Equations), diploma thesis, University of Konstanz, 1998
J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer Verlag, New York et al., 1994
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
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© Copyright 2004
American Mathematical Society
