Preface 1. Introduction 2. Conservation laws and differential equations 3. Characteristics and Riemann problems for linear hyperbolic equations 4. Finite-volume methods 5. Introduction to the CLAWPACK software 6. High resolution methods 7. Boundary conditions and ghost cells 8. Convergence, accuracy, and stability 9. Variable-coefficient linear equations 10. Other approaches to high resolution 11. Nonlinear scalar conservation laws 12. Finite-volume methods for nonlinear scalar conservation laws 13. Nonlinear systems of conservation laws 14. Gas dynamics and the Euler equations 15. Finite-volume methods for nonlinear systems 16. Some nonclassical hyperbolic problems 17. Source terms and balance laws 18. Multidimensional hyperbolic problems 19. Multidimensional numerical methods 20. Multidimensional scalar equations 21. Multidimensional systems 22. Elastic waves 23. Finite-volume methods on quadrilateral grids Bibliography Index.

https://depts.washington.edu/clawpack/book2/sample.pdf

Finite Volume Methods for Hyperbolic Problems

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Asymptotic Analysis of Periodic Structures

1. Basic convexity 2. Boundary structure 3. Minkowski addition 4. Curvature measure and quermass integrals 5. Mixed volumes 6. Inequalities for mixed volumes 7. Selected applications Appendix.

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Convex bodies : the Brunn-Minkowski theory

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

http://ieeexplore.ieee.org/iel5/6354/16969/00781867.pdf

Photonic crystals

For the observation or control of solutions of second-order hyperbolic equation in $\mathbb{R}_t \times \Omega $, Ralston’s construction of localized states [Comm. Pure Appl. Math., 22 (1969), pp. ...

Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary

/pdf/exponential-decay-of-solutions-to-hyperbolic-equations-in-47ph0i9mp8.pdf

Exponential Decay of Solutions to Hyperbolic Equations in Bounded Domains

https://deepblue.lib.umich.edu/bitstream/handle/2027.42/22152/0000583.pdf;sequence=1

Potential and scattering theory on wildly perturbed domains

The theory of maximal positive boundary value problems for symmetric positive systems is developed assuming that the boundary is characteristic of constant multiplicity. No such hypothesis is needed on a neighborhood of the boundary. Both regularity theorems and mixed initial boundary value problems are discussed. Many classical ideas are sharpened in the process.

/pdf/symmetric-positive-systems-with-boundary-characteristic-of-isziijc9de.pdf

Symmetric positive systems with boundary characteristic of constant multiplicity

This paper establishes conditions for the differentiability of solutions to mixed problems for first order hyperbolic systems of the form (3/3» — 2 Aja/dxj — B)u = F on [0, r] X ß, Mu g on [0,7\"] x 3Í2, u(0, x) f(x), x e Q. Assuming that X1 a priori inequalities are known for this equation, it is shown that if F e H'([0, T] x Q), g e H'*l'2([0, T] X 3ñ),/ e H'(Q) satisfy the natural compatibility conditions associated with this equation, then the solution is of class C from [0, T] to H'~f(Q), 0 < p < s. These results are applied to mixed problems with distribution initial data and to quasi-linear mixed problems.

https://www.ams.org/tran/1974-189-00/S0002-9947-1974-0340832-0/S0002-9947-1974-0340832-0.pdf

Jeffrey Rauch

Papers

Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary

Exponential Decay of Solutions to Hyperbolic Equations in Bounded Domains

Potential and scattering theory on wildly perturbed domains

Symmetric positive systems with boundary characteristic of constant multiplicity

Differentiability of solutions to hyperbolic initial-boundary value problems