Decay of solutions for the equations of isothermal gas dynamics
The equations of isothermical gas dynamics are expressed by the system \(u_ t+(k^ 2/v)_ x=0\), \(v_ t-u_ x=0\) of nonlinear hyperbolic conservation laws possessing a convex entropy. The author establishes conservation shock waves and rarefaction waves, using some results of Glimm, Nishida, DiPerna and others. He proves the uniformly boundedness of the total amount of wave interaction. The main aim of the paper is the proof of the fact, that the total variation of the solution to the above problem for the initial data having not necessarily small oscillations decays to zero at the rate \(t^{-1/2}\).
uniformly boundedness of the total amount of wave interaction
scientific article; zbMATH DE number 446765