The semigroup approach to first order quasilinear equations in several space variables. (English) Zbl 0246.35018


35F20 Nonlinear first-order PDEs
47F05 General theory of partial differential operators
47J05 Equations involving nonlinear operators (general)
Full Text: DOI


[1] Ph. Benilan,Solutions intégrales d’equations d’évolution dans un espace de Banach, C.R. Acad. Sci. Paris,274 (1972), 47–50. · Zbl 0246.47068
[2] H. Brezis,Perturbations non linéaires d’operateurs maximaux monotones, C. R. Acad. Sci. Paris269 (1969), 566–569.
[3] H. Brezis andW. Strauss, to appear.
[4] E. Conway andJ. Smoller,Global solutions of the Cauchy problem for quasilinear first order equations in several space variables, Comm. Pure Appl. Math.19 (1966), 95–105. · Zbl 0138.34701
[5] M. G. Crandall,A generalized domain for semigroup generators, Proc. Amer. Math. Soc., to appear. · Zbl 0285.47044
[6] M. G. Crandall,Semigroups of nonlinear transformations in Banach spaces, Contributions to Nonlinear Functional Analysis, 157–179, Educardo H. Zarantonello, Editor, Academic Press, New York and London, 1971.
[7] M. G. Crandall, MRC Technical Summary Report, in preparation.
[8] M. G. Crandall andT. M. Liggett,Generation of semi-groups of nonlinear transformation on general Banach spaces, Amer. J. Math.,93 (1971), 265–298. · Zbl 0226.47038
[9] M. G. Crandall andA. Pazy,Nonlinear evolution equations in Banach spaces, Israel J. Math.11 (1972), 57–94. · Zbl 0249.34049
[10] A. Douglis,Layering methods for nonlinear partial differential equations of first order, Ann. Inst. Fourier. · Zbl 0228.35020
[11] T. Kato,Nonlinear semi-groups and evolution equations, J. Math. Soc. Japan19 (1967), 508–520. · Zbl 0163.38303
[12] Y. Konishi,Nonlinear semigroups in Banach lattices, Proc. Japan Acad.47 (1971), 24–28. · Zbl 0219.47061
[13] S. N. Kružkov,First order quasilinear equations in several independent variables. Math. USSR-Sb.10 (1970), 217–243. · Zbl 0215.16203
[14] B. Quinn,Solutions with shocks: An example of an L 1-contractive semigroup Comm. Pure Appl. Math.24 (1971), 125–132. · Zbl 0209.12401
[15] G. Stampacchia,Equations Elliptiques du Second Ordre a Coefficients Discontinus, Les Presses de L’Université de Montreal, Montreal, 1966. · Zbl 0151.15501
[16] A. I. Vol’pert,The spaces BV and quasilinear equations, Math. USSR-Sb.,2 (1967), 225–267. · Zbl 0168.07402
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.