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Stability of generalized solutions to equations of one-dimensional motion of viscous heat-conducting gases

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Abstract

Nonhomogeneous initial boundary value problems for a specific quasilinear system of equations of composite type are studied. The system describes the one-dimensional motion of a viscous perfect polytropic gas. We assume that the initial data belong to the spacesL ∞(Ω) orL 2(Ω) and the problems under consideration have generalized solutions only. For such solutions, a theorem on strong stability is proved, i.e., estimates for the norm of the difference of two solutions are expressed in terms of the sums of the norms of the differences of the corresponding data. Uniqueness of generalized solutions is a simple consequence of this theorem.

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Authors and Affiliations

  1. Moscow Power Engineering Institute, Technical University, USSR

    A. A. Zlotnik & A. A. Amosov

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  1. A. A. Zlotnik
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  2. A. A. Amosov
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Translated fromMatematicheskie Zametki, Vol. 63, No. 6, pp. 835–846, June, 1998.

This research was supported by the Russian Foundation for Basic Research under grants No. 96-01-00621 and No. 97-01-00214, and by the INTAS Foundation under grant No. 93-27-16.

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Zlotnik, A.A., Amosov, A.A. Stability of generalized solutions to equations of one-dimensional motion of viscous heat-conducting gases. Math Notes 63, 736–746 (1998). https://doi.org/10.1007/BF02312766

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