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This book is the outcome of a conference held at the Centro De Giorgi of the Scuola Normale of Pisa in September 2012. The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. Particular attention was paid to self-similar solutions, such as solitons and travelling waves, asymptotic behaviour, formation of singularities and qualitative properties of solutions. These problems arise in many models from Physics, Biology, Image Processing and Applied Mathematics in general, and have attracted a lot of attention in recent years.

Differential equations, Partial. --- Geometry, Differential. --- Image analysis. --- Stochastic partial differential equations. --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Differential equations, Partial --- Differential equations, Nonlinear --- Mathematics. --- Partial differential equations. --- Calculus of variations. --- Partial Differential Equations. --- Calculus of Variations and Optimal Control; Optimization. --- Differential equations, partial. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Partial differential equations --- Isoperimetrical problems --- Variations, Calculus of

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The present collection is the very first contribution of this type in the field of sparse recovery. Compressed sensing is one of the important facets of the broader concept presented in the book, which by now has made connections with other branches such as mathematical imaging, inverse problems, numerical analysis and simulation. The book consists of four lecture notes of courses given at the Summer School on "Theoretical Foundations and Numerical Methods for Sparse Recovery" held at the Johann Radon Institute for Computational and Applied Mathematics in Linz, Austria, in September 2009. This unique collection will be of value for a broad community and may serve as a textbook for graduate courses. From the contents: "Compressive Sensing and Structured Random Matrices" by Holger Rauhut "Numerical Methods for Sparse Recovery" by Massimo Fornasier "Sparse Recovery in Inverse Problems" by Ronny Ramlau and Gerd Teschke "An Introduction to Total Variation for Image Analysis" by Antonin Chambolle, Vicent Caselles, Daniel Cremers, Matteo Novaga and Thomas Pock

Sparse matrices --- Equations --- Differential equations, Partial --- Numerical solutions --- Numerical solutions