The third boundary value problem for a nonlinear system of second order hyperbolic integro-differential equations

Andrzej Borzymowski

Mathematica Slovaca (1998)

  • Volume: 48, Issue: 3, page 271-283
  • ISSN: 0139-9918

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Borzymowski, Andrzej. "The third boundary value problem for a nonlinear system of second order hyperbolic integro-differential equations." Mathematica Slovaca 48.3 (1998): 271-283. <http://eudml.org/doc/34476>.

@article{Borzymowski1998,
author = {Borzymowski, Andrzej},
journal = {Mathematica Slovaca},
keywords = {Neumann problem; local existence of solutions; Schauder fixed point theorem},
language = {eng},
number = {3},
pages = {271-283},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {The third boundary value problem for a nonlinear system of second order hyperbolic integro-differential equations},
url = {http://eudml.org/doc/34476},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Borzymowski, Andrzej
TI - The third boundary value problem for a nonlinear system of second order hyperbolic integro-differential equations
JO - Mathematica Slovaca
PY - 1998
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 48
IS - 3
SP - 271
EP - 283
LA - eng
KW - Neumann problem; local existence of solutions; Schauder fixed point theorem
UR - http://eudml.org/doc/34476
ER -

References

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  2. CHEN, CH.-WAHL W. VON., Das Rand-Anfangswertproblem für quasilineare Wellengleichungen in Sobolevräumen niedriger Ordnung, J. Reine Angew. Math. 337 (1982), 77-112. (1982) Zbl0486.35053MR0676043
  3. IKAWA M., On the mixed problem for hyperbolic equations of second order with the Neumann boundary conditions, Osaka J. Math. 7 (1970), 203-223. (1970) MR0283395
  4. LADYZHENSKAYA O. A., Mixed ProЫem for a Hyperbolic Equation, Gos. Izd. Techn.-Teoret. Lit., Moscow, 1953. (Russian) (1953) 
  5. LASIECKA J.-STAHEL A., The wave equation with semilinear Neumann boundary conditions, Nonlinear Anal. 15 (1990), 39-58. (1990) Zbl0738.35044MR1058769
  6. LIONS J. L.-MAGENES E., Non-homogeneous Boundary Value Problems and Applications, Springer-Verlag, Berlin-Heidelberg-New York, 1972. (1972) Zbl0227.35001
  7. MIYATAKE S., On the mixed problem for hyperbolic equations of second order with the Neumann boundary condition, J. Math. Kyoto Univ. 13 (1973), 435-487. (1973) MR0333467
  8. MAKSUDOV F. G.-KHUDAVERIEV F. K., A study of multidimensional mixed problem for a class of nonlinear hyperbolic equations, Dokl. Akad. Nauk SSSR 310 (1990), 539-542. (Russian) (1990) 
  9. SHIBATA Y.-TSUTSUMI Y., Local existence of solution of the initial boundary value problem of fully nonlinear wave equation, Nonlinear Anal. 11 (1987), 335-365. (1987) MR0881723
  10. SHIBATA Y., On the Neumann problem for some linear hyperbolic system of 2nd order with coefficients in Sobolev spaces, Tsukuba J. Math. 13 (1989), 283-352. (1989) MR1030219
  11. SHIBATA Y.-KIKUCHI M., On the mixed problem for some quasi-linear hyperbolic system with fully nonlinear boundary condition, J. Differential Equations 80 (1989), 154-197. (1989) MR1003254
  12. SHIBATA Y.-NAHAMURA G., On a local existence theorem of Neumann problem for some quasilinear hyperbolic system of 2nd order, Math. Z. 202 (1989), 1-64. (1989) Zbl0652.35077MR1007739
  13. SZMYDT Z., Sur un nouveau type des problemes pour un systéme d'equations differentielles hyperboliques du second ordre á deux variables indépendantes, Bull. Acad. Polon. Sci. CI. Ill 4 (1956), 67-72. (1956) MR0085434
  14. WEIDEMAIER P., Existence of regular solutions for a quasi-linear wave equation with the third boundary condition, Math. Z. 191 (1985), 449-465. (191) MR0824445

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