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Solutions with shocks: An example of an $$L_ 1$$-contractive semigroup. (English) Zbl 0206.10401

##### MSC:
 35L67 Shocks and singularities for hyperbolic equations 35L65 Hyperbolic conservation laws
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##### References:
 [1] Nonlinear hyperbolic Cauchy problems without convexity condition, Thesis, University of Michigan, 1969. [2] Conway, Comm. Pure Appl. Math. 19 pp 95– (1966) [3] Douglis, Comm. Pure Appl. Math. 12 pp 87– (1959) [4] Hopf, J. Math. Mech. 19 pp 483– (1969) [5] Kato, Jour. Math. Soc. Japan 19 pp 508– (1967) [6] Krushkov, Dokl. Akad. Nauk 187 pp 29– (1969) [7] Lax, Comm. Pure Appl. Mth. 10 pp 537– (1957) [8] Oleinik, Uspekhi Mat. Nauk 12 pp 3– (1957) [9] English translation Amer. Math. Soc. Transl. Ser 2 26 pp 95– [10] Vol’pert, Math. Sbor. 73 pp 255– (1967) [11] (English translation Amer. Math. Soc. Transl. (New Series) 2, 1967, pp. 225–267.) [12] and , Accretive sets and differential equations in Banach spaces, to appear. [13] The logarithmic derivative and equations of evolution in a Banach space, to appear.
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