The Cauchy problem for a first-order quasilinear equation in the class of Besicovitch almost periodic functions

E. Yu. Panov

Novgorod State University after Yaroslav the Wise

Abstract: The existence and uniqueness of a generalized entropy solution in the class of Besicovitch almost periodic functions is proved for the Cauchy problem for a multidimensional inhomogeneous quasilinear equation of the first order.
Bibliography: 12 titles.

Keywords: first order quasilinear equation, generalized entropy solution, Besicovitch almost periodic function, spectrum.

UDC: 517.956

MSC: 35B15, 35L60

Received: 20.01.2017 and 17.05.2017

DOI: 10.4213/sm8915

 English version: Sbornik: Mathematics, 2017, 208:8, 1207–1224

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