Proceedings of the NATO Advanced Study Institute on PDEs in Models of Superfluidity, Superconductivity and Reactive Flows, held in Cargèse, France, from 21 June to 3 July 1999
Nonlinear partial differential equations abound in modern physics. The problems arising in these fields lead to fascinating questions and, at the same time, progress in understanding the mathematical structures is of great importance to the models. Nevertheless, activity in one of the approaches is not always sufficiently in touch with developments in the other field. The book presents the joint efforts of mathematicians and physicists involved in modelling reactive flows, in particular superconductivity and superfluidity. Certain contributions are fundamental to an understanding of such cutting-edge research topics as rotating Bose-Einstein condensates, Kolmogorov-Zakharov solutions for weak turbulence equations, and the propagation of fronts in heterogeneous media.
I.- A two-species reaction-diffusion problem with one static reactant: the case of higher order kinetics.- The influence of advection on the propagation of fronts for reaction-diffusion equations.- Instabilities and Nonlinear Patterns of Overdriven Detonations in Gases.- Ends of Laminar Flamelets: Their Structure, Behaviour and Implications.- On some reaction-diffusion systems with nonlinear diffusion arising in biology.- Control of weakly blowing up semilinear heat equations.- Spirals in Excitable Media.- Conical-shaped travelling fronts allied to the mathematical analysis of the shape of premixed Bunsen flames.- Numerical Modelling of High Speed and Low Speed Combustion.- Lectures on Wave Turbulence and Intermittency.- Overdetermined elliptic problems in physics.- Partial Differential Equations in thin film Flows in Fluid dynamics and rivulets.- II.- The Ginzburg-Landau system for superconducting thin films.- Symmetric Vortex solutions in the U(1) and SO(5) Ginzburg-Landau Models of Superconductivity.- Vortices and sound waves for the Gross-Pitaevskii equation.- A priori estimates for Ginzburg-Landau solutions.- Asymptotic Analysis of Models of Superconductivity.- Spatial Unfolding of Homoclinic Bifurcations.- Existence and long time behaviour of solutions for a homogeneous quantum Boltzmann equation.- Asymptotic behavior in a model of dispersive wave turbulence.- Some problems in superconductivity and reacting flow.- Finite time blow-up of solutions of kinetic equations and formation of Bose-Einstein condensate.- Second order phase transitions.- Vortex Analysis in the Ginzburg-Landau Model of Superconductivity.- On Chern-Simons vortex theory.
Inhaltsverzeichnis
I.- A two-species reaction-diffusion problem with one static reactant: the case of higher order kinetics.- The influence of advection on the propagation of fronts for reaction-diffusion equations.- Instabilities and Nonlinear Patterns of Overdriven Detonations in Gases.- Ends of Laminar Flamelets: Their Structure, Behaviour and Implications.- On some reaction-diffusion systems with nonlinear diffusion arising in biology.- Control of weakly blowing up semilinear heat equations.- Spirals in Excitable Media.- Conical-shaped travelling fronts allied to the mathematical analysis of the shape of premixed Bunsen flames.- Numerical Modelling of High Speed and Low Speed Combustion.- Lectures on Wave Turbulence and Intermittency.- Overdetermined elliptic problems in physics.- Partial Differential Equations in thin film Flows in Fluid dynamics and rivulets.- II.- The Ginzburg-Landau system for superconducting thin films.- Symmetric Vortex solutions in the U(1) and SO(5) Ginzburg-Landau Models of Superconductivity.- Vortices and sound waves for the Gross-Pitaevskii equation.- A priori estimates for Ginzburg-Landau solutions.- Asymptotic Analysis of Models of Superconductivity.- Spatial Unfolding of Homoclinic Bifurcations.- Existence and long time behaviour of solutions for a homogeneous quantum Boltzmann equation.- Asymptotic behavior in a model of dispersive wave turbulence.- Some problems in superconductivity and reacting flow.- Finite time blow-up of solutions of kinetic equations and formation of Bose-Einstein condensate.- Second order phase transitions.- Vortex Analysis in the Ginzburg-Landau Model of Superconductivity.- On Chern-Simons vortex theory.
Klappentext
Nonlinear partial differential equations abound in modern physics. The problems arising in these fields lead to fascinating questions and, at the same time, progress in understanding the mathematical structures is of great importance to the models. Nevertheless, activity in one of the approaches is not always sufficiently in touch with developments in the other field. The book presents the joint efforts of mathematicians and physicists involved in modelling reactive flows, in particular superconductivity and superfluidity. Certain contributions are fundamental to an understanding of such cutting-edge research topics as rotating Bose-Einstein condensates, Kolmogorov-Zakharov solutions for weak turbulence equations, and the propagation of fronts in heterogeneous media.
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