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We study the structure of solutions of Riemann problems for systems of two conservation laws. Such a solution comprises a sequence of elementary waves, viz., rarefaction and shock waves of various types; shock waves are required to have viscous profiles. We construct a Riemann solution by solving a system of equations characterizing its component waves. A… (More)

- E Isaacson, D Marchesin, B Plohr, And B Temple
- 1988

The purpose of this paper is to classify the solutions of Riemann problems near a hyperbolic singularity in a nonlinear system of conservation laws. Hyperbolic singularities play the role in the theory of Riemann problems that rest points play in the theory of ordinary differential equations: Indeed, generically, only a finite number of structures can… (More)

- A V Azevedo, D Marchesin, B Plohr, And K Zumbrun
- 1997

We determine the bifurcation from the constant solution of nonclassical transitional and overcompressive viscous shock prooles, in regions of strict hyperbolicity. Whereas classical shock waves in systems of conservation laws involve a single characteristic eld, nonclassical waves involve two elds in an essential way. This feature is reeected in the viscous… (More)

- Dan Marchesin, Instituto De, Matemática Pura, Ap Licada, Bradleyy J Plohr, Univ At +1 other
- 2008

Program Committee following review of information contained in an abstract submitted by t he author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as prese nted, does not necessarily reflect any position of the Society of Petroleum Engineers,… (More)

The Schatten p-norm condition of the discrete-time Lyapunov operator L A defined on matrices P 2 R nn by L A P P ? APA T is studied for stable matrices A 2 R nn. Bounds are obtained for the norm of L A and its inverse that depend on the spectrum, singular values and radius of stability of A. Since the solution P of the the discrete-time algebraic Lyapunov… (More)

We investigate solutions of Riemann problems for systems of two conservation laws in one spatial dimension. Our approach is to organize Riemann solutions into strata of successively higher codimension. The codimension-zero stratum consists of Riemann solutions that are structurally stable: the number and types of waves in a solution are preserved under… (More)

We investigate a general mechanism, utilizing nonclassical shock waves, for nonuniqueness of solutions of Riemann initial-value problems for systems of two conservation laws. This nonuniqueness occurs whenever there exists a pair of viscous shock waves forming a 2-cycle, i.e., two states U 1 and U 2 such that a traveling wave leads from U 1 to U 2 and… (More)

New upper bounds for the solution of the discrete algebraic Lyapunov equation (DALE) P = APA T + Q are presented. The only restriction on their applicability is that A be stable; there are no restrictions on the singular values of A nor on the diagonalizability of A. The new bounds relate the size of P to the radius of stability of A. The upper bounds are… (More)

Acknowledgements Although this work correctly bears my name as sole author, a thesis is much more than just a text, and cannot be done in isolation. I have been chasing a doctorate for the last seven years, and I got much help along the way. The help I got from the following people and institutions had direct innuence on what I nally wrote down. Jonas de… (More)