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.
@article{bwmeta1.element.bwnjournal-article-bcpv27z1p169bwm,
author = {Glazatov, Sergey},
title = {On some variational inequalities for nonclassical type operators},
journal = {Banach Center Publications},
volume = {27},
year = {1992},
pages = {169-174},
zbl = {0822.35099},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv27z1p169bwm}
}
Glazatov, Sergey. On some variational inequalities for nonclassical type operators. Banach Center Publications, Tome 27 (1992) pp. 169-174. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv27z1p169bwm/
[000] [1] A. B. Aliev, Variational inequalities for quasilinear hyperbolic type operators, Mat. Zametki 42 (3) (1987), 369-380 (in Russian).
[001] [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).
[002] [3] A. B. Aliev, Global solvability of one-sided problems for quasilinear hyperbolic type equations, ibid. 298 (5) (1988), 1033-1036 (in Russian).
[003] [4] G. Duvaut et J.-L. Lions, Les inéquations en mécanique et en physique, Dunod, Paris 1972. | Zbl 0298.73001
[004] [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).
[005] [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). | Zbl 0777.76044
[006] [7] S. Klainerman and A. Majda, Formation of singularities for wave equations, Comm. Pure Appl. Math. 33 (1980), 241-264. | Zbl 0443.35040
[007] [8] R. Landes, Quasilinear hyperbolic variational inequalities, Arch. Rational Mech. Anal. 91 (3) (1986), 267-272.
[008] [9] N. A. Lar'kin, On global solutions of nonlinear hyperbolic inequalities, Dokl. Akad. Nauk SSSR 250 (4) (1980), 806-809 (in Russian).
[009] [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).
[010] [11] J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris 1969. | Zbl 0189.40603
[011] [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). | Zbl 0511.35060
[012] [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).