J. Diaz, Laurent Veron, Existence Theory and Qualitative Properties of the Solutions of some First Order Quasilinear Variational Inequalities, Indiana Univ. Math. J. 32 (1983), 319-361


Abstract

pdf version of the abstract

References

[1] Ph. Benilan, Equations d'évolutions dans un espace de Banach et applications, Thèse d'Etat, Université d'Orsay, 1972.

[2] Ph. Benilan, Equations quasilinéaires du premier ordre, (preprint).

[3] Ph. Benilan and M. G. Crandall, Regularizing effects of homogeneous evolution equations.

[4] A. Bensoussan and J. L. Lions, Inéquations variationnelles non linéaires du premier et du second ordre, C. R. Acad. Sci. Paris Sér. A-B, 276 (1973), pp. A1411–A1415. MathSciNet.

[5] A. Bensoussan and J. L. Lions, On the support of the solution of some variational inequalities of evolution, J. Math. Soc. Japan, 28, No. 1 (1976), pp. 1–17. MathSciNet. Zentralblatt für Mathematik.

[6] H. Brezis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland Publishing Co., Amsterdam, 1973, p. vi+183. MathSciNet. Zentralblatt für Mathematik.

[7] Haim Brezis, Monotone operators, nonlinear semigroups and applications, Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974), Vol. 2, Canad. Math. Congress, Montreal, Que., 1975, pp. 249–255. MathSciNet. Zentralblatt für Mathematik.

[8] Haim Brezis and Ivar Ekeland, Un principe variationnel associé à certaines équations paraboliques. Le cas indépendant du temps, C. R. Acad. Sci. Paris Sér. A-B, 282, No. 17 (1976), p. Aii, A971–A974. MathSciNet. Zentralblatt für Mathematik.

[9] H. Brezis and A. Friedman, Estimates on the support of solutions of parabolic variational inequalities, Illinois J. Math., 20, No. 1 (1976), pp. 82–97. MathSciNet. Zentralblatt für Mathematik.

[10] Edward Conway and Joel Smoller, Clobal solutions of the Cauchy problem for quasi-linear first-order equations in several space variables, Comm. Pure Appl. Math., 19 (1966), pp. 95–105. MathSciNet. Zentralblatt für Mathematik.

[11] Michael G. Crandall, The semigroup approach to first order quasilinear equations in several space variables, Israel J. Math., 12 (1972), pp. 108–132. MathSciNet. Zentralblatt für Mathematik.

[12] M. G. Crandall and T. M. Liggett, Generation of semi-groups of nonlinear transformations on general Banach spaces, Amer. J. Math., 93 (1971), pp. 265–298. MathSciNet. Zentralblatt für Mathematik.

[13] C. M. Dafermos, Generalized characteristics and the structure of solutions of hyperbolic conservation laws, Indiana Univ. Math. J., 26, No. 6 (1977), pp. 1097–1119. MathSciNet. Zentralblatt für Mathematik.

[14] C. M. Dafermos, Asymptotic behaviour of solutions of hyperbolic balance laws, Bifurcation Phenomena in Mathematical Physics and Related Topics, C. Bardos and D. Bessio, eds., Reidel Publishing Co., 1978.

[15] J. I. Diaz, Propriedades cualitativas de ciertos problemas parabolicos no lineales, una classification para los modelos de difusion del color, Real Acad. Cienc. Madrid, XIV (1980).

[16] J. I. Diaz, Tecnica de supersoluciones locales para problemas estacionarios non lineales. Applicacion al estudio de ftujos subsonicos, Real Acad. Cienc. Madrid, XVI (1982).

[17] Nelson Dunford and Jacob L. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York, 1958, p. xiv+858. MathSciNet.

[18] L. C. Evans, Nonlinear evolution equations in an arbitrary Banach space, Israel J. Math., 26, No. 1 (1977), pp. 1–42. MathSciNet. Zentralblatt für Mathematik.

[19] L. C. Evans and B. Knerr, Instantaneous shrinking of the support of nonnegative solutions to certain nonlinear parabolic equations and variational inequalities, Illinois J. Math., 23, No. 1 (1979), pp. 153–166. MathSciNet. Zentralblatt für Mathematik.

[20] M. A. Herrero, Sobre el comportamiento asintotico de ciertos problemas parabolicos, Read Acad. Cienc. Madrid, (to appear).

[21] S. N. Kruzkov, First order quasilinear equations in several independent variables, Math. USSR-Sb., 10 (1970), pp. 217–243.

[22] Peter D. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1973, C.B.M.S. Regional Conferences Series in Applied Math., 11. MathSciNet. Zentralblatt für Mathematik.

[23] O. A. Oleinik, Discontinuous solutions of non-linear differential equations, Uspehi Mat. Nauk (N.S.), 12, No. 3(75) (1957), pp. 3–73. MathSciNet.

[24] B. F. Quinn, Solutions with shocks: An example of an L1-contractive semigroup, Comm. Pure Appl. Math., 24 (1971), pp. 125–132. MathSciNet. Zentralblatt für Mathematik.

[25] L. Veron, Équations d'évolution semi-linéaires du second ordre dans L1, Rev. Roumaine Math. Pures Appl., 27, No. 1 (1982), pp. 95–123. MathSciNet. Zentralblatt für Mathematik.

[26] L. Veron, Effets régularisants de semi-groupes non linéaires dans des espaces de Banach, Ann. Fac. Sci. Toulouse Math. (5), 1, No. 2 (1979), pp. 171–200. MathSciNet. Zentralblatt für Mathematik.

[27] L. Veron, Some remarks on the convergence of approximate solutions of nonlinear evolution equations in Hilbert spaces, Math. Comp., 39, No. 160 (1982), pp. 325–337. MathSciNet. Zentralblatt für Mathematik.

[28] L. Veron, Weak weak-star compactness of dominated subsets of Lμ1(E;Lν(F)), Houston J. Math., 9, No. 4 (1983), pp. 581–586. MathSciNet. Zentralblatt für Mathematik.

[29] A. I. Vol'pert, The space B.V. and quasilinear equations, Math. USSR-Sb., 2 (1967), pp. 225–267. Zentralblatt für Mathematik.

To read this abstract...
IE 6.0 Strictly conforms to W3C stylesheets
IE 5.5 Download Math Player in order to render MathML; does not conform to W3C stylesheets
Mozilla 1.0 Strictly conforms to W3C stylesheets
Netscape 7.0 Install fonts in order to render MathML

Valid XHTML 1.0!