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Explicit construction of measure solutions of Cauchy problem for transportation equations

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Abstract

The transportation equations are a mathematical model of zero-pressure flow in gas dynamics and the adhesion particle dynamics system to explain the formation of large scale structures in the universe. With the help of convex hull of a potential function, the solution is explicitly constructed here. It is straightforward to prove that the solution is a global measure one. And Dirac delta-shocks explained as the concentration of particles may develop in the solution.

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Authors and Affiliations

  1. Department of Mathematics, Ningbo University, 315211, Ningbo, China

    Shaozhong Cheng

  2. Institute of Applied Mathematics, Chinese Academy of Sciences, 100080, Bei**g, China

    Jiequan Li

  3. Institute of Mathematics, Chinese Academy of Sciences, 100080, Bei**g, China

    Tong Zhang

Authors
  1. Shaozhong Cheng
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  2. Jiequan Li
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  3. Tong Zhang
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Project supported by the Institute of Mathematics, Chinese Academy of Sciences and by the National Fundamental Research Program of State Commission of Science and Technology of China, and Chinese Academy of Sciences.

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Cheng, S., Li, J. & Zhang, T. Explicit construction of measure solutions of Cauchy problem for transportation equations. Sci. China Ser. A-Math. 40, 1287–1299 (1997). https://doi.org/10.1007/BF02876374

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  • DOI: https://doi.org/10.1007/BF02876374

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