Renormalized entropy solutions of the Cauchy problem for a first-order inhomogeneous quasilinear equation

E. Yu. Panov

Novgorod State University after Yaroslav the Wise

Abstract: The concept of a renormalized entropy solution of the Cauchy problem for an inhomogeneous quasilinear equation of the first order is introduced. Existence and uniqueness theorems are proved, together with a comparison principle. Connections with generalized entropy solutions are investigated.
Bibliography: 10 titles.

Keywords: first-order quasilinear equations, generalized entropy solutions, comparison principle, renormalized solutions, existence and uniqueness.

UDC: 517.956.35

MSC: Primary 35F25, 35D30; Secondary 35B51

Received: 30.01.2013 and 15.05.2013

DOI: 10.4213/sm8217

 English version: Sbornik: Mathematics, 2013, 204:10, 1480–1515

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