Analytical and Numerical Aspects of Partial Differential Equations (eBook)

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Etienne Emmrich and Petra Wittbold , Technical University Berlin.

Etienne Emmrich und Petra Wittbold, TU Berlin.

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

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"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