Uniform decay for a hyperbolic system with differential inclusion and nonlinear memory source term on the boundary

Jong Yeoul Park; Sun Hye Park

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 2, page 287-303
  • ISSN: 0011-4642

Abstract

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We prove the existence and uniform decay rates of global solutions for a hyperbolic system with a discontinuous and nonlinear multi-valued term and a nonlinear memory source term on the boundary.

How to cite

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Park, Jong Yeoul, and Park, Sun Hye. "Uniform decay for a hyperbolic system with differential inclusion and nonlinear memory source term on the boundary." Czechoslovak Mathematical Journal 59.2 (2009): 287-303. <http://eudml.org/doc/37924>.

@article{Park2009,
abstract = {We prove the existence and uniform decay rates of global solutions for a hyperbolic system with a discontinuous and nonlinear multi-valued term and a nonlinear memory source term on the boundary.},
author = {Park, Jong Yeoul, Park, Sun Hye},
journal = {Czechoslovak Mathematical Journal},
keywords = {existence of solution; differential inclusion; memory source term; uniform decay; existence; differential inclusion; memory source term; uniform decay},
language = {eng},
number = {2},
pages = {287-303},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Uniform decay for a hyperbolic system with differential inclusion and nonlinear memory source term on the boundary},
url = {http://eudml.org/doc/37924},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Park, Jong Yeoul
AU - Park, Sun Hye
TI - Uniform decay for a hyperbolic system with differential inclusion and nonlinear memory source term on the boundary
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 2
SP - 287
EP - 303
AB - We prove the existence and uniform decay rates of global solutions for a hyperbolic system with a discontinuous and nonlinear multi-valued term and a nonlinear memory source term on the boundary.
LA - eng
KW - existence of solution; differential inclusion; memory source term; uniform decay; existence; differential inclusion; memory source term; uniform decay
UR - http://eudml.org/doc/37924
ER -

References

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  1. Aassila, M., Global existence of solutions to a wave equation with damping and source terms, Diff. Int. Eqs. 14 (2001), 1301-1314. (2001) Zbl1018.35053MR1859607
  2. Cavalcanti, M. M., Existence and uniform decay for the Euler-Bernoulli viscoelastic equation with nonlocal boundary dissipation, Discrete Contin. Dynam. Systems 8 (2002), 675-695. (2002) Zbl1009.74034MR1897875
  3. Cavalcanti, M. M., Cavalcanti, V. N. Domingos, Ma, T. F., Soriano, J. A., Global existence and asymptotic stability for viscoelastic problems, Diff. Int. Eqs. 15 (2002), 731-748. (2002) MR1893844
  4. Gasiński, L., 10.1016/S0022-247X(02)00431-6, J. Math. Anal. Appl. 276 (2002), 723-746. (2002) MR1944786DOI10.1016/S0022-247X(02)00431-6
  5. Gasiński, L., Papageorgiou, N. S., 10.1006/jmaa.1999.6701, J. Math. Anal. Appl. 244 (2000), 200-213. (2000) MR1746797DOI10.1006/jmaa.1999.6701
  6. Kormornik, V., Zuazua, E., A direct method for the boundary stabilization of the wave equation, J. Math. Pures et Appl. 69 (1990), 33-54. (1990) MR1054123
  7. Lions, J. L., Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod-Gauthier Villars, Paris (1969). (1969) Zbl0189.40603MR0259693
  8. Miettinen, M., 10.1016/0362-546X(94)00312-6, Nonlinear Anal. 26 (1996), 725-734. (1996) Zbl0858.35072MR1362746DOI10.1016/0362-546X(94)00312-6
  9. Miettinen, M., Panagiotopoulos, P. D., On parabolic hemivariational inequalities and applications, Nonlinear Anal. 35 (1999), 885-915. (1999) Zbl0923.35089MR1664899
  10. Rivera, J. E. Munoz, Salvatierra, A. P., Asymptotic behavior of the energy in partially viscoelastic materials, Quart. Appl. Math. 59 (2001), 557-578. (2001) MR1848535
  11. Panagiotopoulos, P. D., Inequality Problems in Mechanics and Applincations, Convex and Nonconvex Energy Functions, Birkhäuser, Basel, Boston (1985). (1985) MR0896909
  12. Panagiotopoulos,, P. D., Hemivariational Inequalities and Applications in Mechanics and Engineering, Springer, New York (1993). (1993) MR1385670
  13. Park, J. Y., Bae, J. J., 10.1016/S0096-3003(01)00031-5, Appl. Math. Comput. 129 (2002), 87-105. (2002) Zbl1032.35139MR1897321DOI10.1016/S0096-3003(01)00031-5
  14. Park, J. Y., Kim, H. M., Park, S. H., 10.1016/S0362-546X(03)00216-5, Nonlinear Anal. 55 (2003), 103-113. (2003) Zbl1032.35144MR2001634DOI10.1016/S0362-546X(03)00216-5
  15. Rauch, J., 10.1090/S0002-9939-1977-0442453-6, Proc. Amer. Math. Soc. 64 (1977), 277-282. (1977) Zbl0413.35031MR0442453DOI10.1090/S0002-9939-1977-0442453-6

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