On a variational inequality for a hyperbolic-parabolic equation with a lipschitzian nonlinearity
DOI:
https://doi.org/10.22199/S07160917.1997.0002.00003Keywords:
Variational inequality, Non-linear operator of hyperbolic-parabolic type, Weak solutionsAbstract
References
[1] Bensoussan, A.and Lions, J. L. and Papanicolaou, G., Pertubations et augmentation des conditions initiales, in: Singular Pertubation and Boundary Layer Theory, Springer- Velarg, Lyon., pp. 10-26, (1976).
[2] Maciel, A. B., On a hyperbolic-parabolic equation with a continuous nonlinearity, Nonlinear Analysis T. M. A., 20, pp. 745-754, (1993).
[3] Kinderlehrer, D. and Stampacchia, G., An Introduction to Variational Inequalities and their Applications, Academic Press, New York, (1980).
[4] Pereira, D. C., Existence, uniqueness and asymptotic behavior for solutions of the nonlinear beam equation, Nonlinear Analysis T. M. A., 14, pp. 613-623, (1990).
[5] Browder, F. E., Nonlinear monotone operators and convex sets in Banach spaces. Bull. Am. Math. Society., 71, pp. 780-785, (1965).
[6] Menzala, G.P. , On global classical solutions of a uonlinear wave equation , Applicable Analys-i.s., lO, pp. 179-195, (1980).
[7] Stampacchia, G., Formes bilineaires sur les cnsembles convexes. C.R. Acad. Sc. Paris., 258, pp. 4413-,1416, (1964).
[8] Brezis, H., Problemes unilatereaux. J. Math. Pures et Appl., 51, pp. 1-168, (1972).
[9] Ferreira, J., Nonlinear hyperbolic-parabolic partial differential equation in noncylindrical domain, Rendiconti del Circolo Matematico di Palermo., 44, pp. 135-146, (1995).
[10] Ferreira, J., On weak solutions of a nonlinear hyperbolic-parabolic partial differential equation. Comp. Appl. Math., 14, N° 3, pp. 1-15, (1995).
[11] Ferreira, J., On weak solutions of semilinear hyperbolic-parabolic equations. lnternational Journal of Mathematics and Mathematical Sciences., 19, n°.4, pp. 751-758, (1996).
[12] Lions, J. L., Quelques méthodes des résolu tions des problem aux limites nonlinéaires, Dunod, Paris, ( 1969).
[13] Lions, J. L. and Starnpacchis, G., Variational inequalities. Com. Pure and Appl., Math. 20, pp. 493-519 (1967).
[14] Limaco, J., On weak solutions of a nonlinear hyperbolic-parabolic equations. Preprint.
[15] Medeiros, L. A., L.A. Remarks on hyperbolic-parabolic partial differential equations, Memória.s de Matemática. 123, IM-UFRJ, (1981).
[16] Medeiros, L. A., L.A. Nonlinear hyperbolic-parabolic partial differential equatious. Funcialaj Ekvacioj., 23, N° 2, pp. 151-158, (1980).
[17] Medeiros, L. A. and Miranda, M. M., Local solutions for a nonlinear unilateral problem, Rev. Roumaine Math. Pures Appl., 31, pp. 371-382, (1 986).
[18] Miranda, M. M. and Lima, O. A., One-sided problem for a nonlinear hyperbolic-parabolic equation, Proceedings of IX CNMAC., Brasília, (1986).
[19] Visik, M. and Ladayzenskaya, 0., On boundary value problem for and certais class of operators equations, Amer. Math. Soc. Transl., 2 N°.10, (1958).
[20] Lar'kin, N. A., N.A. Boundary problem in the large for a class of hyperbolic-parabolic equation, Sib. Math. J., 18 N° 6, pp. 1003-1006, (1977).
[21] Lar'kin, N. A., lnequalities for degenerating hyperbolic operators, Sib. Math. J., 21, N° 4, pp. 613-617, (1980).
[22] Lar'kin, N. A. and Novikov. V. A.. and Yanenko, N. N .. Towards a Theory of Variable-Type Equations, in: Numerical Methods in Fluid Dynamics. (N.N. Yanenko and Yu. l. Shokiu Editores), Moscow, Mir., pp. 315-335, (1984).
[23] Vragov, N., On a rnixed problem of a hyperbolic-parabolic equations, Dokl. Akad. Nauk. USSR., 224 N° 2, pp. 1179-1183, (1975).
[24] Lima, O. A., Existence and uniqueness of solutions for an abstract nonlinear hyperbolic-parabolic equation, Applicable Analysis., 24, pp. 101-106, (1987).
[25] Ebihara, Y., Modified variational inequalities to sernilinear wave equations. Nonlinear Analys'is., 7, N° 8, pp. 821-826, (1983).
[26] Ebihara, Y. and Medeiros, L. A. and Miranda, M. M., On a variational inequality for a nonlinear operator of hyperbolic type, Bol. 8oc. Mat., 16, pp. 41-54, (1985).
[2] Maciel, A. B., On a hyperbolic-parabolic equation with a continuous nonlinearity, Nonlinear Analysis T. M. A., 20, pp. 745-754, (1993).
[3] Kinderlehrer, D. and Stampacchia, G., An Introduction to Variational Inequalities and their Applications, Academic Press, New York, (1980).
[4] Pereira, D. C., Existence, uniqueness and asymptotic behavior for solutions of the nonlinear beam equation, Nonlinear Analysis T. M. A., 14, pp. 613-623, (1990).
[5] Browder, F. E., Nonlinear monotone operators and convex sets in Banach spaces. Bull. Am. Math. Society., 71, pp. 780-785, (1965).
[6] Menzala, G.P. , On global classical solutions of a uonlinear wave equation , Applicable Analys-i.s., lO, pp. 179-195, (1980).
[7] Stampacchia, G., Formes bilineaires sur les cnsembles convexes. C.R. Acad. Sc. Paris., 258, pp. 4413-,1416, (1964).
[8] Brezis, H., Problemes unilatereaux. J. Math. Pures et Appl., 51, pp. 1-168, (1972).
[9] Ferreira, J., Nonlinear hyperbolic-parabolic partial differential equation in noncylindrical domain, Rendiconti del Circolo Matematico di Palermo., 44, pp. 135-146, (1995).
[10] Ferreira, J., On weak solutions of a nonlinear hyperbolic-parabolic partial differential equation. Comp. Appl. Math., 14, N° 3, pp. 1-15, (1995).
[11] Ferreira, J., On weak solutions of semilinear hyperbolic-parabolic equations. lnternational Journal of Mathematics and Mathematical Sciences., 19, n°.4, pp. 751-758, (1996).
[12] Lions, J. L., Quelques méthodes des résolu tions des problem aux limites nonlinéaires, Dunod, Paris, ( 1969).
[13] Lions, J. L. and Starnpacchis, G., Variational inequalities. Com. Pure and Appl., Math. 20, pp. 493-519 (1967).
[14] Limaco, J., On weak solutions of a nonlinear hyperbolic-parabolic equations. Preprint.
[15] Medeiros, L. A., L.A. Remarks on hyperbolic-parabolic partial differential equations, Memória.s de Matemática. 123, IM-UFRJ, (1981).
[16] Medeiros, L. A., L.A. Nonlinear hyperbolic-parabolic partial differential equatious. Funcialaj Ekvacioj., 23, N° 2, pp. 151-158, (1980).
[17] Medeiros, L. A. and Miranda, M. M., Local solutions for a nonlinear unilateral problem, Rev. Roumaine Math. Pures Appl., 31, pp. 371-382, (1 986).
[18] Miranda, M. M. and Lima, O. A., One-sided problem for a nonlinear hyperbolic-parabolic equation, Proceedings of IX CNMAC., Brasília, (1986).
[19] Visik, M. and Ladayzenskaya, 0., On boundary value problem for and certais class of operators equations, Amer. Math. Soc. Transl., 2 N°.10, (1958).
[20] Lar'kin, N. A., N.A. Boundary problem in the large for a class of hyperbolic-parabolic equation, Sib. Math. J., 18 N° 6, pp. 1003-1006, (1977).
[21] Lar'kin, N. A., lnequalities for degenerating hyperbolic operators, Sib. Math. J., 21, N° 4, pp. 613-617, (1980).
[22] Lar'kin, N. A. and Novikov. V. A.. and Yanenko, N. N .. Towards a Theory of Variable-Type Equations, in: Numerical Methods in Fluid Dynamics. (N.N. Yanenko and Yu. l. Shokiu Editores), Moscow, Mir., pp. 315-335, (1984).
[23] Vragov, N., On a rnixed problem of a hyperbolic-parabolic equations, Dokl. Akad. Nauk. USSR., 224 N° 2, pp. 1179-1183, (1975).
[24] Lima, O. A., Existence and uniqueness of solutions for an abstract nonlinear hyperbolic-parabolic equation, Applicable Analysis., 24, pp. 101-106, (1987).
[25] Ebihara, Y., Modified variational inequalities to sernilinear wave equations. Nonlinear Analys'is., 7, N° 8, pp. 821-826, (1983).
[26] Ebihara, Y. and Medeiros, L. A. and Miranda, M. M., On a variational inequality for a nonlinear operator of hyperbolic type, Bol. 8oc. Mat., 16, pp. 41-54, (1985).
Published
2018-04-04
How to Cite
[1]
J. Ferreira, “On a variational inequality for a hyperbolic-parabolic equation with a lipschitzian nonlinearity”, Proyecciones (Antofagasta, On line), vol. 16, no. 2, pp. 125-139, Apr. 2018.
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