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The δ′ wave solution to a totally degenerate system of conservation laws

Author

Listed:
  • Pang, Yicheng
  • Shao, Liuyang
  • Wen, Yongsong
  • Ge, Jianjun

Abstract

We focus on the Riemann solutions to a totally degenerate system of conservation laws with repeated eigenvalues and repeated eigenvectors. Based on the theory of multiplication of distributions, we define α-solution to this system within a convenient space of distributions, and then establish both the expressions of the α-solutions and the condition of occurrence of each α-solution to this system. With these results, we solve the Riemann problem and then obtain all of exact solutions which are independent of α. It is shown that the delta wave issues in the solution. It is also noticed that both the delta wave and the vacuum state arise simultaneously in the solution. Moreover, the δ′ wave emerges in the solution. Finally, the exact solutions agree with the corresponding numerical solutions.

Suggested Citation

  • Pang, Yicheng & Shao, Liuyang & Wen, Yongsong & Ge, Jianjun, 2022. "The δ′ wave solution to a totally degenerate system of conservation laws," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005124
    DOI: 10.1016/j.chaos.2022.112302
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