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Title: On a regularization of a scalar conservation law with discontinuous coefficients

This paper is devoted to a scalar conservation law with a linear flux function involving discontinuous coefficients. It is clear that the delta standing wave should be introduced into the Riemann solution in some nonclassical situation. In order to study the formation of delta standing wave, we consider a regularization of the discontinuous coefficient with the Helmholtz mollifier and then obtain a regularized system which depends on a regularization parameter ε > 0. The regularization mechanism is a nonlinear bending of characteristic curves that prevents their finite-time intersection. It is proved rigorously that the solutions of regularized system converge to the delta standing wave solution in the ε → 0 limit. Compared with the classical method of vanishing viscosity, here it is clear to see how the delta standing wave forms naturally along the characteristics.
Authors:
 [1]
  1. School of Mathematics and Statistics Science, Ludong University, Yantai 264025 (China)
Publication Date:
OSTI Identifier:
22251096
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPARATIVE EVALUATIONS; DIAGRAMS; FUNCTIONS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; STANDING WAVES