Geodesic
Stability and Convergence of the Difference Schemes for Equations of Isentropic Gas Dynamics in Lagrangian Coordinates
Publications de l'Institut Mathématique, _N_S_91 (2012) no. 105, p. 137 .

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For the the initial-boundary value problem (IBVP) for the isentropic gas dynamics written in Lagrangian coordinates in Riemann invariants we show how the necessary conditions for existence of global smooth solution can be obtained using technics due to P.\,Lax. Under these conditions we formulate the existence result in the class of piecewise-smooth functions. A priori estimates with respect to the input data for the difference scheme approximating this problem are obtained. Stability estimates are proved using only limitations for the initial and boundary conditions corresponding the differential problem. Estimates of stability in the general case have been obtained only for the finite instant of time $t
Classification : 65N06 65M12
Keywords: Isentropic gas dynamics, Riemann invariants, Lagrangian coordinates, initial-boundary value problem, well-posedness and blow-up, finite difference scheme, stability 
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     author = {Piotr Matus and Dmitry Polyakov},
     title = {Stability and {Convergence} of the {Difference} {Schemes}  for {Equations} of {Isentropic} {Gas} {Dynamics} in {Lagrangian} {Coordinates}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {137 },
     publisher = {mathdoc},
     volume = {_N_S_91},
     number = {105},
     year = {2012},
     language = {en},
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Piotr Matus; Dmitry Polyakov. Stability and Convergence of the Difference Schemes  for Equations of Isentropic Gas Dynamics in Lagrangian Coordinates. Publications de l'Institut Mathématique, _N_S_91 (2012) no. 105, p. 137 . http://geodesic.mathdoc.fr/item/PIM_2012_N_S_91_105_a11/