zbMATH — the first resource for mathematics

A kinetic construction of global solutions of first order quasilinear equations. (English) Zbl 0519.35053

MSC:
 35L65 Hyperbolic conservation laws 35A35 Theoretical approximation in context of PDEs 82B40 Kinetic theory of gases in equilibrium statistical mechanics 35L45 Initial value problems for first-order hyperbolic systems
Full Text:
References:
 [1] E. Conway and J. Smoller, Clobal solutions of the Cauchy problem for quasi-linear first-order equations in several space variables , Comm. Pure Appl. Math. 19 (1966), 95-105. · Zbl 0138.34701 · doi:10.1002/cpa.3160190107 [2] M. G. Crandall, The semigroup approach to first order quasilinear equations in several space variables , Israel J. Math. 12 (1972), 108-132. · Zbl 0246.35018 · doi:10.1007/BF02764657 [3] M. G. Crandall and A. Majda, Monotone difference approximations for scalar conservation laws , Math. Comp. 34 (1980), no. 149, 1-21. JSTOR: · Zbl 0423.65052 · doi:10.2307/2006218 · links.jstor.org [4] A. Douglis, Layering methods for nonlinear partial differential equations of first order , Ann. Inst. Fourier (Grenoble) 22 (1972), no. 3, 141-227. · Zbl 0242.35014 · doi:10.5802/aif.428 · numdam:AIF_1972__22_3_141_0 · eudml:74087 [5] E. Giusti, Minimal surfaces and functions of bounded variation , Department of Pure Mathematics, Australian National University, Canberra, 1977. · Zbl 0402.49033 [6] E. Hopf, The partial differential equation $$u_ t+uu_ x=\mu u_ xx$$ , Comm. Pure Appl. Math. 3 (1950), 201-230. · Zbl 0039.10403 · doi:10.1002/cpa.3160030302 [7] A. Kaniel, A kinetic model for a mono-atomic gas , [8] S. N. Kružkov, First order quasilinear equations in several independent variables , Math. USSR-Sb. 10 (1970), 217-243. · Zbl 0215.16203 · doi:10.1070/SM1970v010n02ABEH002156 [9] P. D. Lax, Hyperbolic systems of conservation laws. II , Comm. Pure Appl. Math. 10 (1957), 537-566. · Zbl 0081.08803 · doi:10.1002/cpa.3160100406 [10] P. D. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves , Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1973. · Zbl 0268.35062 [11] S. Ôharu and T. Takahashi, A convergence theorem of nonlinear semigroups and its application to first order quasilinear equations , J. Math. Soc. Japan 26 (1974), 124-160. · Zbl 0265.47052 · doi:10.2969/jmsj/02610124 [12] O. A. Oleĭ nik, Discontinuous solutions of non-linear differential equations , Amer. Math. Soc. Transl. (2) 26 (1963), 95-172. · Zbl 0131.31803 [13] B. K. Quinn, Solutions with shocks: An example of an $$L_1$$-contractive semigroup , Comm. Pure Appl. Math. 24 (1971), 125-132. · Zbl 0209.12401 · doi:10.1002/cpa.3160240203
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.