Explicit construction of measure solutions of Cauchy problem for transportation equations

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...

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Published inScience China. Mathematics Vol. 40; no. 12; pp. 1287 - 1299
Main Author 陈绍仲 李杰权 张同
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.12.1997
Subjects
Cauchy
Cauchy problems
convex
Convexity
delta-shocks
Dirac
equations
Gas dynamics
hull
measure
problem
solution
Transportation
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Summary: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.
Bibliography:11-5837/O1
CHENG Shaozhong(Department of Mathematics,Ningbo University,Ningbo 315211,China) LI Jiequan(Institute of Applied Mathematics,Chinese Academy of Sciences,Beijing 100080,China)and ZHANG Tong(Institute of Mathematics,Chinese Academy of Sciences,Beijing 100080,China)
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ISSN:1674-7283
1006-9283
1869-1862
1862-2763
DOI:10.1007/BF02876374