Elementary Interactions in Quasi-linear Hyperbolic Systems

نویسندگان

  • CLEVE MOLER
  • JOEL SMOLLER
  • L. CESARI
چکیده

where t>0, o o < x < o o , U(t, x)=(u(t, x), v(t, x)), and the function F(U)= (f(u, v), g(u, v)) is smooth. GLIMM [2] has proved existence of a weak solution provided that the variation of the initial data Uo(x) is small. GLIMM & LAX [3] then improved this result by requiring that the oscillation of Uo(x) be small. SMOLLER [7] has proved the existence of a weak solution provided that Uo(x ) is constant except for a single arbitrary jump (the Riemann problem). Finally, NISmDA [6] has proved existence for general data Uo but for the special case f= l / v , g=u. Here we will prove existence under the assumption that Uo(x) is constant except for two jumps; that is, Uo (x) is of the form

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تاریخ انتشار 2004