Emmrich / Wittbold Analytical and Numerical Aspects of Partial Differential Equations

Notes of a Lecture Series
1. Auflage 2009
ISBN: 978-3-11-021210-5
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 300 Seiten, Gewicht: 10 g

Reihe: De Gruyter Proceedings in Mathematics

This text contains a series of self-contained reviews on the state of the art in different areas of partial differential equations, presented by French mathematicians. Topics include qualitative properties of reaction-diffusion equations, multiscale methods coupling atomistic and continuum mechanics, adaptive semi-Lagrangian schemes for the Vlasov-Poisson equation, and coupling of scalar conservation laws.

Zielgruppe

Researchers, Graduate Students of Mathematics; Academic Libraries

Autoren/Hrsg.

Emmrich, Etienne

Wittbold, Petra

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik

Inhaltsverzeichnis

1;Frontmatter;1
2;Table of contents;6
3;S. N. Kruzhkov’s lectureson first-order quasilinear PDEs;7
3.1;Introduction;8
3.2;1 Derivation of the equations;8
3.3;2 The local classical theory;11
3.4;3 Classical (smooth) solutions of the Cauchy problem and formation of singularities;15
3.5;4 Generalized solutions of quasilinear equations;24
3.6;5 The notion of generalized entropy solution;36
3.7;6 The Riemann problem (evolution of a primitive jump);56
3.8;Afterword;66
3.9;Acknowledgments;69
3.10;References;71
4;Standing waves in nonlinear Schrödinger equations;157
4.1;1 Introduction;157
4.2;2 The Cauchy problem;160
4.3;3 Existence, uniqueness and properties of solitons;163
4.4;4 Stability;172
4.5;5 Instability;183
4.6;6 Appendix;189
4.7;References;195
5;Multiscale methods coupling atomistic and continuum mechanics: some examples of mathematical analysis;199
5.1;1 Introduction;199
5.2;2 Models;202
5.3;3 From an atomistic model to a continuum model;205
5.4;4 Atomistic to continuum coupling;208
5.5;5 Discussion;228
5.6;References;243
6;Maximal regularity and applications to PDEs;253
7;Index;295

Über Autor(innen)

Etienne Emmrich und Petra Wittbold, TU Berlin.

Etienne Emmrich und Petra Wittbold, TU Berlin.