Analytical and Numerical Aspects of Partial Differential Equations: Notes of a Lecture Series

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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.

Author(s): Etienne Emmrich, Petra Wittbold, Etienne Emmrich
Series: De Gruyter Proceedings in Mathematics
Edition: 1
Publisher: Walter de Gruyter
Year: 2009

Language: English
Pages: 296
Tags: Математика;Дифференциальные уравнения;Дифференциальные уравнения в частных производных;

Frontmatter
......Page 1
Table of contents......Page 6
S. N. Kruzhkov’s lectures on first-order quasilinear PDEs......Page 7
Adaptive semi-Lagrangian schemes for Vlasov equations......Page 75
Coupling of a scalar conservation law with a parabolic problem......Page 121
Standing waves in nonlinear Schrödinger equations......Page 157
Multiscale methods coupling atomistic and continuum mechanics: some examples of mathematical analysis......Page 199
Maximal regularity and applications to PDEs......Page 253
Backmatter
......Page 295