Ebook: Nonlinear PDE’s in Condensed Matter and Reactive Flows

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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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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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.
Content:
Front Matter....Pages i-xi
A Two-Species Reaction-Diffusion Problem with One Static Reactant: The Case of Higher Order Kinetics....Pages 1-10
The Influence of Advection on the Propagation of Fronts in Reaction-Diffusion Equations....Pages 11-48
Instabilities and Nonlinear Patterns of Overdriven Detonations in Gases....Pages 49-97
Ends of Laminar Flamelets: Their Structure, Behaviour and Implications....Pages 99-113
On Some Reaction-Diffusion Systems with Nonlinear Diffusion Arising in Biology....Pages 115-125
Control of Weakly Blowing up Semilinear Heat Equations....Pages 127-148
Spirals in Excitable Media....Pages 149-167
Conical-Shaped Travelling Fronts Allied to the Mathematical Analysis of the Shape of Premixed Bunsen Flames....Pages 169-187
Numerical Modelling of High Speed and Low Speed Combustion....Pages 189-226
Lectures on Wave Turbulence and Intermittency....Pages 227-271
Overdetermined Elliptic Problems in Physics....Pages 273-295
Partial Differential Equations in Thin Film Flows in Fluid Dynamics and Rivulets....Pages 297-312
The Ginzburg-Landau System for Superconducting Thin Films....Pages 313-321
Symmetric Vortex Solutions in the U(1) and SO(5) Ginzburg-Landau Models of Superconductivity....Pages 323-337
Vortices and Sound Waves for the Gross-Pitaevskii Equation....Pages 339-354
A Priori Estimates for Ginzburg-Landau Solutions....Pages 355-373
Asymptotic Analysis of Models of Superconductivity....Pages 375-398
Spatial Unfolding of Homoclinic Bifurcations....Pages 399-412
Existence and Long Time Behaviour of Solutions for A Homogeneous Quantum Boltzmann Equation....Pages 413-428
Asymptotic Behavior in a Model of Dispersive Wave Turbulence....Pages 429-447
Some Problems in Superconductivity and Reacting Flow....Pages 449-459
Finite Time Blow-up of Solutions of Kinetic Equations and Formation of Bose-Einstein Condensate....Pages 461-472
Second Order Phase Transitions....Pages 473-490
Vortex Analysis in the Ginzburg-Landau Model of Superconductivity....Pages 491-506
On Chern-Simons Vortex Theory....Pages 507-526

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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.
Content:
Front Matter....Pages i-xi
A Two-Species Reaction-Diffusion Problem with One Static Reactant: The Case of Higher Order Kinetics....Pages 1-10
The Influence of Advection on the Propagation of Fronts in Reaction-Diffusion Equations....Pages 11-48
Instabilities and Nonlinear Patterns of Overdriven Detonations in Gases....Pages 49-97
Ends of Laminar Flamelets: Their Structure, Behaviour and Implications....Pages 99-113
On Some Reaction-Diffusion Systems with Nonlinear Diffusion Arising in Biology....Pages 115-125
Control of Weakly Blowing up Semilinear Heat Equations....Pages 127-148
Spirals in Excitable Media....Pages 149-167
Conical-Shaped Travelling Fronts Allied to the Mathematical Analysis of the Shape of Premixed Bunsen Flames....Pages 169-187
Numerical Modelling of High Speed and Low Speed Combustion....Pages 189-226
Lectures on Wave Turbulence and Intermittency....Pages 227-271
Overdetermined Elliptic Problems in Physics....Pages 273-295
Partial Differential Equations in Thin Film Flows in Fluid Dynamics and Rivulets....Pages 297-312
The Ginzburg-Landau System for Superconducting Thin Films....Pages 313-321
Symmetric Vortex Solutions in the U(1) and SO(5) Ginzburg-Landau Models of Superconductivity....Pages 323-337
Vortices and Sound Waves for the Gross-Pitaevskii Equation....Pages 339-354
A Priori Estimates for Ginzburg-Landau Solutions....Pages 355-373
Asymptotic Analysis of Models of Superconductivity....Pages 375-398
Spatial Unfolding of Homoclinic Bifurcations....Pages 399-412
Existence and Long Time Behaviour of Solutions for A Homogeneous Quantum Boltzmann Equation....Pages 413-428
Asymptotic Behavior in a Model of Dispersive Wave Turbulence....Pages 429-447
Some Problems in Superconductivity and Reacting Flow....Pages 449-459
Finite Time Blow-up of Solutions of Kinetic Equations and Formation of Bose-Einstein Condensate....Pages 461-472
Second Order Phase Transitions....Pages 473-490
Vortex Analysis in the Ginzburg-Landau Model of Superconductivity....Pages 491-506
On Chern-Simons Vortex Theory....Pages 507-526
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