Singularities: Formation, Structure, and Propagation - J. Eggers

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Résumé :
This book explores a wide range of singular phenomena, providing mathematical tools for understanding them and highlighting their common features.

Biographie:
J. Eggers is Professor of Applied Mathematics at the University of Bristol. His career has been devoted to the understanding of self-similar phenomena, and he has more than fifteen years of experience in teaching non-linear and scaling phenomena to undergraduate and postgraduate students. Eggers has made fundamental contributions to our mathematical understanding of free-surface flows, in particular the break-up and coalescence of drops. His work was instrumental in establishing the study of singularities as a research field in applied mathematics and in fluid mechanics. He is a member of the Academy of Arts and Sciences in Erfurt, Germany, a fellow of the American Physical Society, and has recently been made a Euromech Fellow.

Sommaire:
Preface; Part I. Setting the Scene: 1. What are singularities all about?; 2. Blow-up; 3. Similarity profile; 4. Continuum equations; 5. Local singular expansions; 6. Asymptotic expansions of PDEs; Part II. Formation of Singularities: 7. Drop break-up; 8. A numerical example: drop pinch-off; 9. Slow convergence; 10. Continuation; Part III. Persistent Singularities ? Propagation: 11. Shock waves; 12. The dynamical system; 13. Vortices; 14. Cusps and caustics; 15. Contact lines and cracks; Appendix A. Vector calculus; Appendix B. Index notation and the summation convention; Appendix C. Dimensional analysis; References; Index.