Analytical and Numerical Aspects of Partial Differential Equations: Notes of a Lecture Series (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. 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 S.N. Kruzhkov's lectures on first-order quasilinear PDEs -- Gregory A. Chechkin and Andrey Yu. Goritsky Adaptive semi-Lagrangian schemes for Vlasov equations -- Martin Campos Pinto Coupling of a scalar conservation law with a parabolic problem -- Julien Jimenez Standing waves in nonlinear Schrodinger equations -- Stefan LeCoz Multiscale methods coupling atomistic and continuum mechanics : some examples of mathematical analysis -- Frederic Legoll Maximal regularity and applications to PDEs -- Sylvie Monniaux. Review text: "The comprehensiveness, integrative nature, and scientific base and approach of the book are impressively, distinctive features having the power to excite attention and shall be highly praised as a remarkable triumph. Superabundantly referenced, it will richly reward the reader's effort."In: Current Engineering Practice 11/2009