Global existence of solutions of the equations of one-dimensional thermoviscoelasticity with initial data in B V and L 1

Jong Uhn Kim

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1983)

  • Volume: 10, Issue: 3, page 357-427
  • ISSN: 0391-173X

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Kim, Jong Uhn. "Global existence of solutions of the equations of one-dimensional thermoviscoelasticity with initial data in $BV$ and $L^1$." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 10.3 (1983): 357-427. <http://eudml.org/doc/83911>.

@article{Kim1983,
author = {Kim, Jong Uhn},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {without dissipation; existence of global solutions in BV; Cauchy problem; one-dimensional nonlinear thermoviscoelasticity with initial conditions given for the displacemet, the velocity, and the temperature; equations reduce to the hyperbolic conservation laws; adding dissipation terms},
language = {eng},
number = {3},
pages = {357-427},
publisher = {Scuola normale superiore},
title = {Global existence of solutions of the equations of one-dimensional thermoviscoelasticity with initial data in $BV$ and $L^1$},
url = {http://eudml.org/doc/83911},
volume = {10},
year = {1983},
}

TY - JOUR
AU - Kim, Jong Uhn
TI - Global existence of solutions of the equations of one-dimensional thermoviscoelasticity with initial data in $BV$ and $L^1$
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1983
PB - Scuola normale superiore
VL - 10
IS - 3
SP - 357
EP - 427
LA - eng
KW - without dissipation; existence of global solutions in BV; Cauchy problem; one-dimensional nonlinear thermoviscoelasticity with initial conditions given for the displacemet, the velocity, and the temperature; equations reduce to the hyperbolic conservation laws; adding dissipation terms
UR - http://eudml.org/doc/83911
ER -

References

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  1. [1] L. Ahlfors, Complex Analysis, 2nd ed., McGraw-Hill, New York, 1966. Zbl0154.31904MR510197
  2. [2] C. Dafermos, Conservation Laws with Dissipation, in Nonlinear Phenomena in Mathematical Sciences, ed. by U. Lakshimikantham, Academic Press. Zbl0529.35054
  3. [3] C. Dafermos, Global smooth solutions to the initial-boundary value problem for the equations of one-dimensional nonlinear thermoviscoelasticity, SIAM J. Math. Anal. (to appear). Zbl0489.73124MR653464
  4. [4] C. Dafermos - L. Hsiao, Global smooth thermomechanical processes in one-dimensional nonlinear thermoviscoelasticity, Nonlinear Analysis (to appear). Zbl0498.35015MR661710
  5. [5] T.P. Liu, Solutions in the large for equations of nonisentropic gas dynamics, Indiana Univ. Math. J., 26 (1977), pp. 137-168. MR435618
  6. [6] J. Kim, Solutions to the equations of one dimensional viscoelasticity in BV, LCDS Report 81-13, Brown University (1981). 
  7. [7] M. Slemrod, Global existence, uniqueness and asymptotic stability of classical smooth solutions in one-dimensional nonlinear thermoelasticity, Arch. Rational Mech. Anal., 76 (1981), pp. 97-134. Zbl0481.73009MR629700
  8. [8] E. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970. Zbl0207.13501MR290095

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