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This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differential equations (PDEs), as well as a set of fundamental open problems for further development.

Shock waves are fundamental in nature. They are governed by the Euler equations or their variants, generally in the form of nonlinear conservation laws--PDEs of divergence form. When a shock hits an...

This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differential equations (PDEs), as well as a set of fundamental open problems for further development.

Shock waves are fundamental in nature. They are governed by the Euler equations or their variants, generally in the form of nonlinear conservation laws--PDEs of divergence form. When a shock hits an...

The volume comprises

This book introduces key concepts in modeling and risk assessments of vapor intrusion, a process by which the subsurface volatile contaminants migrate into the building of concern. Soil vapor intrusion is the major exposure pathway for building occupants to chemicals from the subsurface, and its risk assessments determine the criteria of volatile contaminants in soil/groundwater in brownfield redevelopment. The chapters feature the recent advances in vapor intrusion studies and practices, including analytical and numerical modeling of vapor intrusion, statistical findings of United States...

This book presents thirteen papers, representing the most significant advances and current trends in nonlinear hyperbolic conservation laws and related analysis with applications. Topics covered include a survey on multidimensional systems of conservation laws as well as novel results on liquid crystals, conservation laws with discontinuous flux functions, and applications to sedimentation. Also included are articles on recent advances in the Euler equations and the Navier-Stokes-Fourier-Poisson system, in addition to new results on collective phenomena described by the Cucker-Smale model....

This book introduces key concepts in modeling and risk assessments of vapor intrusion, a process by which the subsurface volatile contaminants migrate into the building of concern. Soil vapor intrusion is the major exposure pathway for building occupants to chemicals from the subsurface, and its risk assessments determine the criteria of volatile contaminants in soil/groundwater in brownfield redevelopment. The chapters feature the recent advances in vapor intrusion studies and practices, including analytical and numerical modeling of vapor intrusion, statistical findings of United States...

This book examines the exciting interface between differential geometry and continuum mechanics, now recognised as being of increasing technological significance. Topics discussed include isometric embeddings in differential geometry and the relation with microstructure in nonlinear elasticity, the use of manifolds in the description of microstructure in continuum mechanics, experimental measurement of microstructure, defects, dislocations, surface energies and nematic liquid crystals. Compensated compactness in partial differential equations is also treated.

The volume is intended for...