Asymptotic stability for a nonlinear evolution equation

Zhang Hongwei; Chen Guowang

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 1, page 101-107
  • ISSN: 0010-2628

Abstract

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We establish the asymptotic stability of solutions of the mixed problem for the nonlinear evolution equation ( | u t | r - 2 u t ) t - Δ u t t - Δ u - δ Δ u t = f ( u ) .

How to cite

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Hongwei, Zhang, and Guowang, Chen. "Asymptotic stability for a nonlinear evolution equation." Commentationes Mathematicae Universitatis Carolinae 45.1 (2004): 101-107. <http://eudml.org/doc/249323>.

@article{Hongwei2004,
abstract = {We establish the asymptotic stability of solutions of the mixed problem for the nonlinear evolution equation $(|u_t|^\{r-2\}u_t)_t-\Delta u_\{tt\}-\Delta u-\delta \Delta u_t=f(u)$.},
author = {Hongwei, Zhang, Guowang, Chen},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {nonlinear evolution equation; mixed problem; asymptotic stability of solutions; nonlinear evolution equation; mixed problem; asymptotic stability of solutions},
language = {eng},
number = {1},
pages = {101-107},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Asymptotic stability for a nonlinear evolution equation},
url = {http://eudml.org/doc/249323},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Hongwei, Zhang
AU - Guowang, Chen
TI - Asymptotic stability for a nonlinear evolution equation
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 1
SP - 101
EP - 107
AB - We establish the asymptotic stability of solutions of the mixed problem for the nonlinear evolution equation $(|u_t|^{r-2}u_t)_t-\Delta u_{tt}-\Delta u-\delta \Delta u_t=f(u)$.
LA - eng
KW - nonlinear evolution equation; mixed problem; asymptotic stability of solutions; nonlinear evolution equation; mixed problem; asymptotic stability of solutions
UR - http://eudml.org/doc/249323
ER -

References

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  3. Cavalcanti M.M., Domingos Cavalcanti V.N., Ferreira J., Existence and uniform decay for a nonlinear viscoelastic equation with strong damping, Math. Meth. Appl. Sci. 24 (2001), 1043-1053. (2001) Zbl0988.35031MR1855298
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  6. Park J.Y., Bae J.J., On solutions of quasilinear wave equations with nonlinear damping terms, Czechoslovak Math. J. 50 (2000), 565-585. (2000) Zbl1079.35533MR1777478
  7. Levine H.A., Pucci P., Serrin J., Some remarks on global nonexistence for nonautonomous abstract evolution equations, Contemporary Mathematics 208 (1997), 253-263. (1997) Zbl0882.35081MR1467010
  8. Pucci P., Serrin J., Stability for abstract evolution equations, in Partial Differential Equation and Applications, P. Marcellimi, et al. (Eds.), Marcel Dekker, 1996, pp.279-288. Zbl0879.47027MR1371599
  9. Pucci P., Serrin J., Asymptotic stability for nonautonomous wave equation, Comm. Pure Appl. Math. XLXX (1996), 177-216. (1996) MR1371927
  10. Payne L.E., Sattinger D.H., Saddle points and unstability of nonlinear hyperbolic equations, Israel J. Math. 22 (1975), 273-303. (1975) MR0402291

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