Nonlinear PDE’s in Condensed Matter and Reactive FlowsHenri Berestycki, Yves Pomeau Springer Science & Business Media, 30 nov. 2002 - 526 pages 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. |
Table des matières
THE CASE OF HIGHER ORDER KINETICS | 1 |
THE INFLUENCE OF ADVECTION ON THE PROPAGATION OF FRONTS IN REACTIONDIFFUSION EQUATIONS | 11 |
INSTABILITIES AND NONLINEAR PATTERNS OF OVERDRIVEN DETONATIONS IN GASES | 49 |
THEIR STRUCTURE BEHAVIOUR AND IMPLICATIONS | 99 |
ON SOME REACTIONDIFFUSION SYSTEMS WITH NONLINEAR DIFFUSION ARISING IN BIOLOGY | 115 |
CONTROL OF WEAKLY BLOWING UP SEMILINEAR HEAT EQUATIONS | 127 |
SPIRALS IN EXCITABLE MEDIA | 149 |
CONICALSHAPED TRAVELLING FRONTS ALLIED TO THE MATHEMATICAL ANALYSIS OF THE SHAPE OF PREMIXED BUNSEN FLAM... | 169 |
SYMMETRIC VORTEX SOLUTIONS IN THE U1 AND SO5 GINZBURGLANDAU MODELS OF SUPERCONDUCTIVITY | 323 |
VORTICES AND SOUND WAVES FOR THE GROSSPITAEVSKII EQUATION | 339 |
A PRIORI ESTIMATES FOR GINZBURGLANDAU SOLUTIONS | 355 |
ASYMPTOTIC ANALYSIS OF MODELS OF SUPERCONDUCTIVITY | 375 |
SPATIAL UNFOLDING OF HOMOCLINIC BIFURCATIONS | 399 |
EXISTENCE AND LONG TIME BEHAVIOUR OF SOLUTIONS FOR A HOMOGENEOUS QUANTUM BOLTZMANN EQUATION | 413 |
ASYMPTOTIC BEHAVIOR IN A MODEL OF DISPERSIVE WAVE TURBULENCE | 429 |
SOME PROBLEMS IN SUPERCONDUCTIVITY AND REACTING FLOW | 449 |
NUMERICAL MODELLING OF HIGH SPEED AND LOW SPEED COMBUSTION | 189 |
LECTURES ON WAVE TURBULENCE AND INTERMITTENCY | 227 |
OVERDETERMINED ELLIPTIC PROBLEMS IN PHYSICS | 273 |
PARTIAL DIFFERENTIAL EQUATIONS IN THIN FILM FLOWS IN FLUID DYNAMICS AND RIVULETS | 297 |
THE GINZBURGLANDAU SYSTEM FOR SUPERCONDUCTING THIN FILMS | 313 |
FINITE TIME BLOWUP OF SOLUTIONS OF KINETIC EQUATIONS AND FORMATION OF BOSEEINSTEIN CONDENSATE | 461 |
SECOND ORDER PHASE TRANSITIONS | 473 |
VORTEX ANALYSIS IN THE GINZBURGLANDAU MODEL OF SUPERCONDUCTIVITY | 491 |
ON CHERNSIMONS VORTEX THEORY | 507 |
Autres éditions - Tout afficher
Nonlinear PDEs in Condensed Matter and Reactive Flows Henri Berestycki,Yves Pomeau Aperçu limité - 2002 |
Nonlinear PDE’s in Condensed Matter and Reactive Flows Henri Berestycki,Yves Pomeau Aperçu limité - 2012 |
Nonlinear Pdes in Condensed Matter and Reactive Flows Henri Berestycki,Yves Pomeau Aucun aperçu disponible - 2011 |
Expressions et termes fréquents
acoustic analysis approximation assume asymptotic asymptotic analysis behavior Berestycki bifurcation Boltzmann equation boundary conditions bounded Carleman inequalities Clavin combustion condensate consider constant corresponding defined denote density described detonation differential equation diffusion dimensional domain dynamics eigenvalue elliptic energy entropy existence Figure finite flame fluid flux function Ginzburg-Landau Ginzburg-Landau equations global heat equation heat release homogeneous initial data instability integral laminar flamelet leading order limit linear Mach number magnetic field Math mathematical maximum principle minimizer nonlinear nonlinear Schrödinger equation normal obtained parameter periodic Phys planar Pomeau premixed flame problem proof propagation reaction reaction-diffusion reaction-diffusion equations Reactive Flows satisfies scale shock soliton spatial spectrum speed stability superconducting superfluid symmetric solutions temperature term Theorem theory traveling fronts unique variables velocity vortex vortices zero