: Etienne Emmrich, Petra Wittbold
: Analytical and Numerical Aspects of Partial Differential Equations Notes of a Lecture Series
: Walter de Gruyter GmbH& Co.KG
: 9783110212105
: De Gruyter Proceedings in Mathematics
: 1
: CHF 177.40
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: Allgemeines, Lexika
: English
: 300
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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.



Etienne EmmrichandPe ra Wittbold , Technical University Berlin.
Frontmatter1
Table of contents6
S. N. Kruzhkov’s lectureson first-order quasilinear PDEs7
Introduction8
1 Derivation of the equations8
2 The local classical theory11
3 Classical (smooth) solutions of the Cauchy problem and formation of singularities15
4 Generalized solutions of quasilinear equations24
5 The notion of generalized entropy solution36
6 The Riemann problem (evolution of a primitive jump)56
Afterword66
Acknowledgments69
References71
Standing waves in nonlinear Schrödinger equations157
1 Introduction157
2 The Cauchy problem160
3 Existence, uniqueness and properties of solitons163
4 Stability172
5 Instability183
6 Appendix189
References195
Multiscale methods coupling atomistic and continuum mechanics: some examples of mathematical analysis199
1 Introduction199
2 Models202
3 From an atomistic model to a continuum model205
4 Atomistic to continuum coupling208
5 Discussion228
References243
Maximal regularity and applications to PDEs253
Index295