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Kružkov-type uniqueness theorem for the chemical flood conservation law system with local vanishing viscosity admissibility

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, 27 Fontanka, 191023, St. Petersburg, Russia

E-mail Address: rastmusician@gmail.com

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Sergey Matveenko

https://orcid.org/0000-0002-3809-0457

Chebyshev Laboratory, St. Petersburg State University, 14th Line V.O., 29, Saint Petersburg 199178, Russia

E-mail Address: matveis239@gmail.com

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https://doi.org/10.1142/S0219891624500164Cited by:0 (Source: Crossref)

Abstract

In this paper, we study the uniqueness of solutions of the initial-boundary value problem in the quarter-plane for the chemical flood conservation law system in the class of piecewise $𝒞^{1}$ -smooth functions under certain restrictions. The vanishing viscosity method is used locally on the discontinuities of the solution to determine admissible and inadmissible shocks. The Lagrangian coordinate transformation is utilized in order to split the equations. The proof of uniqueness is based on an entropy inequality similar to the one used in the classical Kružkov’s theorem.

Communicated by R. M. Colombo

Keywords:

AMSC: 35L50, 35L65, 35L67, 76L05

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