Displaying similar documents to “Classical solutions to the scalar conservation law with discontinuous initial data”

The p-system II: The vacuum

Robin Young (2003)

Banach Center Publications

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We consider the equations of isentropic gas dynamics in Lagrangian coordinates. We are interested in global interactions of large waves, and their relation to global solvability and well-posedness for large data. One of the main difficulties in this program is the possible occurrence of a vacuum, in which the specific volume is infinite. In this paper we show that the vacuum cannot be generated in finite time. More precisely, if the vacuum is present for some positive time, then it must...

Wave front tracking in systems of conservation laws

Rinaldo M. Colombo (2004)

Applications of Mathematics

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This paper contains several recent results about nonlinear systems of hyperbolic conservation laws obtained through the technique of Wave Front Tracking.

Well-posedness for Systems Representing Electromagnetic/Acoustic Wavefront Interaction

H. T. Banks, J. K. Raye (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we consider dispersive electromagnetic systems in dielectric materials in the presence of acoustic wavefronts. A theory for existence, uniqueness, and continuous dependence on data is presented for a general class of systems which include acoustic pressure-dependent Debye polarization models for dielectric materials.

Hyperbolic systems of conservation laws.

Alberto Bressan (1999)

Revista Matemática Complutense

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This is a survey paper, written in the occasion of an invited talk given by the author at the Universidad Complutense in Madrid, October 1998. Its purpose is to provide an account of some recent advances in the mathematical theory of hyperbolic systems of conservation laws in one space dimension. After a brief review of basic concepts, we describe in detail the method of wave-front tracking approximation and present some of the latest results on uniqueness and stability of entropy weak...