Books by Alberto Bressan
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This work provides a self-contained introduction to the mathematical theory of hyperbolic systems of conservation laws, with particular emphasis on the study of discontinuous solutions characterized by the appearance of shock waves.
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This volume contains the proceedings of the Summer Program on Nonlinear Conservation Laws and Applications held at the IMA on July 13--31, 2009. Hyperbolic conservation laws is a classical subject, which has experienced vigorous growth in recent years. The present collection prov...ides a timely survey of the state of the art in this exciting field, and a comprehensive outlook on open problems. Contributions of more theoretical nature cover the following topics: global existence and uniqueness theory of one-dimensional systems, multidimensional conservation laws in several space variables and approximations of their solutions, mathematical analysis of fluid motion, stability and dynamics of viscous shock waves, singular limits for viscous systems, basic principles in the modeling of turbulent mixing, transonic flows past an obstacle and a fluid dynamic approach for isometric embedding in geometry, models of nonlinear elasticity, the Monge problem, and transport equations with rough coefficients. In addition, there are a number of papers devoted to applications. These include: models of blood flow, self-gravitating compressible fluids, granular flow, charge transport in fluids, and the modeling and control of traffic flow on networks.
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Contains the proceedings of the Summer Program on Nonlinear Conservation Laws and Applications held at the IMA on July 13 - 31, 2009.
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With Applications to Linear Partial Differential Equations. Addressed to graduate students in mathematics or other disciplines who wish to understand the essential concepts of functional analysis and their applications of partial differential equations.
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In recent years flows in networks have attracted the interest of many researchers from different areas, e.g. The main reason for this ubiquity is the wide and diverse range of applications, such as vehicular traffic, supply chains, blood flow, irrigation channels, data networks a...nd others.
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A guide to intertwined developments of control theory and nonsmooth analysis.
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Deals with the Center Manifold Theorem. This title provides a review of hyperbolic conservation laws. It introduces the vanishing viscosity approach and explains the building blocks of the theory in particular the crucial role of the decomposition by travelling waves.
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