On some variational inequalities for nonclassical type operators

Sergey Glazatov

Banach Center Publications (1992)

  • Volume: 27, Issue: 1, page 169-174
  • ISSN: 0137-6934

Abstract

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The purpose of this paper is to make a brief review of results obtained in the theory of variational inequalities for nonclassical operators, namely, of degenerate hyperbolic and variable type.

How to cite

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Glazatov, Sergey. "On some variational inequalities for nonclassical type operators." Banach Center Publications 27.1 (1992): 169-174. <http://eudml.org/doc/262823>.

@article{Glazatov1992,
abstract = {The purpose of this paper is to make a brief review of results obtained in the theory of variational inequalities for nonclassical operators, namely, of degenerate hyperbolic and variable type.},
author = {Glazatov, Sergey},
journal = {Banach Center Publications},
keywords = {nonclassical operators},
language = {eng},
number = {1},
pages = {169-174},
title = {On some variational inequalities for nonclassical type operators},
url = {http://eudml.org/doc/262823},
volume = {27},
year = {1992},
}

TY - JOUR
AU - Glazatov, Sergey
TI - On some variational inequalities for nonclassical type operators
JO - Banach Center Publications
PY - 1992
VL - 27
IS - 1
SP - 169
EP - 174
AB - The purpose of this paper is to make a brief review of results obtained in the theory of variational inequalities for nonclassical operators, namely, of degenerate hyperbolic and variable type.
LA - eng
KW - nonclassical operators
UR - http://eudml.org/doc/262823
ER -

References

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  1. [1] A. B. Aliev, Variational inequalities for quasilinear hyperbolic type operators, Mat. Zametki 42 (3) (1987), 369-380 (in Russian). 
  2. [2] A. B. Aliev, One sided problems for quasilinear hyperbolic operators in function spaces, Dokl. Akad. Nauk SSSR 297 (2) (1987), 271-275 (in Russian). 
  3. [3] A. B. Aliev, Global solvability of one-sided problems for quasilinear hyperbolic type equations, ibid. 298 (5) (1988), 1033-1036 (in Russian). 
  4. [4] G. Duvaut et J.-L. Lions, Les inéquations en mécanique et en physique, Dunod, Paris 1972. Zbl0298.73001
  5. [5] S. Glazatov, On a class of quasilinear hyperbolic inequalities, in: Some Applications of Functional Analysis to Problems of Mathematical Physics, Inst. Math., Siberian Branch Acad. Sci. U.S.S.R., Novosibirsk 1990, 67-80 (in Russian). 
  6. [6] S. Glazatov, A variational inequality connected with a variable type nonlinear equation, in: Dynamics of Continuous Media 99, Inst. Hydrodynamics, Siberian Branch Acad. Sci. U.S.S.R., Novosibirsk 1990, 18-33 (in Russian). Zbl0777.76044
  7. [7] S. Klainerman and A. Majda, Formation of singularities for wave equations, Comm. Pure Appl. Math. 33 (1980), 241-264. Zbl0443.35040
  8. [8] R. Landes, Quasilinear hyperbolic variational inequalities, Arch. Rational Mech. Anal. 91 (3) (1986), 267-272. 
  9. [9] N. A. Lar'kin, On global solutions of nonlinear hyperbolic inequalities, Dokl. Akad. Nauk SSSR 250 (4) (1980), 806-809 (in Russian). 
  10. [10] N. A. Lar'kin, A one-sided problem for a nonlocal quasilinear hyperbolic equation arising in the theory of elasticity, ibid. 274 (6) (1984), 1341-1344 (in Russian). 
  11. [11] J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris 1969. Zbl0189.40603
  12. [12] F. G. Maksudov, A. B. Aliev and D. M. Takhirov, A one-sided problem for a quasilinear equation of hyperbolic type, Dokl. Akad. Nauk SSSR 258 (4) (1981), 789-791 (in Russian). Zbl0511.35060
  13. [13] S. Pyatkov, Solvability of boundary value problems for a nonlinear degenerate elliptic equation, in: Applications of Functional Analysis to Nonclassical Equations of Mathematical Physics, Inst. Math., Siberian Branch Acad. Sci. U.S.S.R., Novosibirsk 1988, 102-117 (in Russian). 

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