Forced vibrations in one-dimensional nonlinear thermoelasticity as a local coercive-like problem

Eduard Feireisl

Commentationes Mathematicae Universitatis Carolinae (1990)

  • Volume: 031, Issue: 2, page 243-255
  • ISSN: 0010-2628

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Feireisl, Eduard. "Forced vibrations in one-dimensional nonlinear thermoelasticity as a local coercive-like problem." Commentationes Mathematicae Universitatis Carolinae 031.2 (1990): 243-255. <http://eudml.org/doc/17842>.

@article{Feireisl1990,
author = {Feireisl, Eduard},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {topological degree of mapping; Lebesgue space; Sobolev spaces of integrable functions; nonlinear operator equation; smooth time-periodic solutions; hyperbolic-parabolic system of equations; Galerkin approximation; finite system of nonlinear equations},
language = {eng},
number = {2},
pages = {243-255},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Forced vibrations in one-dimensional nonlinear thermoelasticity as a local coercive-like problem},
url = {http://eudml.org/doc/17842},
volume = {031},
year = {1990},
}

TY - JOUR
AU - Feireisl, Eduard
TI - Forced vibrations in one-dimensional nonlinear thermoelasticity as a local coercive-like problem
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1990
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 031
IS - 2
SP - 243
EP - 255
LA - eng
KW - topological degree of mapping; Lebesgue space; Sobolev spaces of integrable functions; nonlinear operator equation; smooth time-periodic solutions; hyperbolic-parabolic system of equations; Galerkin approximation; finite system of nonlinear equations
UR - http://eudml.org/doc/17842
ER -

References

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  2. Day W. A., Steady forced vibrations in coupled thermoelasticity, Arch. Rational Mech. Anal. 93 (1986), 323-334. (1986) Zbl0597.73008MR0829832
  3. DiPerna R. J., Convergence of approximate solutions to conservation laws, Arch. Rational Mech. Anal. 82 (1983), 27-70. (1983) Zbl0519.35054MR0684413
  4. Greenberg J. M., MacCamy R. C., Mizel V. J., On the existence, uniqueness and stability of solutions of the equation ρ χ t t = E ( χ x ) χ x x + λ χ x x , J. Math. Mech. 17 (1968), 707-728. (1968) MR0225026
  5. Kato T., Locally coercive nonlinear equations, with applications to some periodic solutions, Duke Math. J. 51 (1984), 923-936. (1984) Zbl0571.47051MR0771388
  6. Klainerman S., Global existence for nonlinear wave equation, Comm. Pure Appl. Math. 33 (1980), 43-101. (1980) MR0544044
  7. Matsumura A., Global existence and asymptotics of the solutions of the second order quasilinear hyperbolic equations with the first order dissipation, Publ. Res. Inst. Math. Soc. 13 (1977), 349-379. (1977) Zbl0371.35030MR0470507
  8. Racke R., Initial boundary value problems in one-dimensional non-linear thermoelasticity, Math. Meth. Appl. Sci. 10 (1988), 517-529. (1988) MR0965419
  9. Rothe E. H., Introduction to various aspects of degree theory in Banach spaces, Providence AMS, 1986. (1986) Zbl0597.47040MR0852987
  10. Shibata Y., On the global existence of classical solutions of mixed problem for some second order nonlinear hyperbolic operators with dissipative term in the interior domain, Funkcialaj Ekvacioj 25 (1982), 303-345. (1982) Zbl0524.35070MR0707564
  11. Slemrod M., Global existence, uniqueness, and asymptotic stability of classical smooth solutions in one-dimensional nonlinear thermoelasticity, Arch. Rational Mech. Anal. 76 (1981), 97-134. (1981) Zbl0481.73009MR0629700
  12. Zheng S., Initial boundary value problems for quasilinear hyperbolic-parabolic coupled systems in higher dimensional spaces, Chinese Ann. of Math. 4B(4) (1983), 443-462. (1983) Zbl0509.35056MR0741742
  13. Zheng S., Global solutions and applications to a class of quasilinear hyperbolic-parabolic coupled system, Scienta Sinka, Ser. A 27 (1984), 1274-1286. (1984) MR0794293
  14. Zheng S., Shen W., Global solutions to the Cauchy problem of quasilinear hyperbolic-parabolic coupled system, Scienta Sinica, Ser. A 10 (1987), 1133-1149. (1987) MR0942420

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