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## Notes of a Lecture Series

**Description**

The topics of the contributions to this book range from an investigation of the qualitative behaviour of solutions of particular partial differential equations to the study of the complexity of numerical methods for the reliable and efficient solution of partial differential equations. A main focus is on nonlinear problems and theoretical studies reflecting recent developments of topical interest.

This book grew out of a series of lectures at the Technische Universität Berlin held by young mathematicians from France who followed an invitation for a short-term stay during the academic years 2007-2009. The book addresses students of mathematics in their last year, PhD students as well as younger researchers working in the field of partial differential equations and their numerical treatment. Most of the contributions only require some basic knowledge in functional analysis, partial differential equations, and numerical analysis.

**Content**

GREGORY A. CHECHKIN AND ANDREY YU. GORITSKY

S. N. Kruzhkov's lectures on first-order quasilinear PDEs

MARTIN CAMPOS PINTO

Adaptive semi-Lagrangian schemes for Vlasov equations

JULIEN JIMENEZ

Coupling of a scalar conservation law with a parabolic problem

STEFAN LE COZ

Standing waves in nonlinear Schrödinger equations

FREDERIC LEGOLL

Multiscale methods coupling atomistic and continuum mechanics: some examples of mathematical analysis

SYLVIE MONNIAUX

Maximal regularity and applications to PDEs