Some problems related to the study of interaction kernels: coagulation, fragmentation and diffusion in kinetic and quantum equations

[1]  J. Israelachvili Intermolecular and surface forces , 1985 .

[2]  L. Diósi Calderia-Leggett master equation and medium temperatures , 1993 .

[3]  J. McLeod On the Scalar Transport Equation , 1964 .

[4]  A. Leggett,et al.  Path integral approach to quantum Brownian motion , 1983 .

[5]  Three eras of micellization. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  George Papanicolaou,et al.  Dynamic Theory of Suspensions with Brownian Effects , 1983 .

[7]  Š.,et al.  On self-similarity and stationary problem for fragmentation and coagulation models , 2022 .

[8]  H. Müller,et al.  Zur allgemeinen Theorie ser raschen Koagulation: Die Koagulation von Stäbchen- und Blättchenkolloiden; die Theorie beliebig polydisperser Systeme und der Strömungskoagulation , 1928 .

[9]  J. M. BalP The Discrete Coagulation-Fragmentation Equations: Existence, Uniqueness, and Density Conservation , 2004 .

[10]  D. Whiffen Thermodynamics , 1973, Nature.

[11]  Philippe Laurençot,et al.  From the discrete to the continuous coagulation–fragmentation equations , 2002, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[12]  M. Smoluchowski Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen , 1918 .

[13]  G. Lindblad On the generators of quantum dynamical semigroups , 1976 .

[14]  Oliver Penrose,et al.  The Becker-Döring equations at large times and their connection with the LSW theory of coarsening , 1997 .

[15]  Philippe Laurençot,et al.  On coalescence equations and related models , 2004 .

[16]  CoalescenceDavid J. Aldous Stochastic Coalescence , 1998 .

[17]  Nicola Bellomo,et al.  MATHEMATICAL TOPICS ON THE MODELLING COMPLEX MULTICELLULAR SYSTEMS AND TUMOR IMMUNE CELLS COMPETITION , 2004 .

[18]  José Alfredo Cañizo Rincón,et al.  Asymptotic behaviour of solutions to the generalized Becker–Döring equations for general initial data , 2005, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[19]  M. Sentís Quantum theory of open systems , 2002 .

[20]  I. Stewart On the coagulation-fragmentation equation , 1990 .

[21]  F. Bouchut Smoothing Effect for the Non-linear Vlasov-Poisson-Fokker-Planck System , 1995 .

[22]  M. Fowler,et al.  Function Spaces , 2022 .

[23]  I. W. Stewart,et al.  A global existence theorem for the general coagulation-fragmentation equation with unbounded kernels , 1989 .

[24]  Jack Carr,et al.  Asymptotic behavior of solutions to the coagulation-fragmentation equations. II. Weak fragmentation , 1994 .

[25]  I. I. Vrabie,et al.  Compactness Methods for Nonlinear Evolutions , 1995 .

[26]  Thierry Goudon,et al.  The Beker-Döring System and Its Lifshitz-Slyozov Limit , 2002, SIAM J. Appl. Math..

[27]  M. Slemrod The Becker-Döring Equations , 2000 .

[28]  Global L1 theory and regularity for the 3D nonlinear Wigner–Poisson–Fokker–Planck system , 2004 .

[29]  F. P. D. Costa,et al.  Asymptotic behaviour of low density solutions to the generalized Becker-Döring equations , 1998 .

[30]  Thierry,et al.  Hydrodynamic Limit for the Vlasov-Navier-Stokes Equations . Part II : Fine Particles Regime coro , 2006 .

[31]  乔花玲,et al.  关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解 , 2003 .

[32]  J. B. McLeod,et al.  ON AN INFINITE SET OF NON-LINEAR DIFFERENTIAL EQUATIONS , 1962 .

[33]  S. Mischler,et al.  From the Becker–Döring to the Lifshitz–Slyozov–Wagner Equations , 2002 .

[34]  J. Nieto,et al.  Global solutions of the mean–field, very high temperature Caldeira–Leggett master equation , 2006 .

[35]  T. Paul,et al.  Sur les mesures de Wigner , 1993 .

[36]  Philippe Laurençot,et al.  Global existence for the discrete diffusive coagulation-fragmentation equations in $L^1$ , 2002 .

[37]  Philippe Laurençot,et al.  On a Class of Continuous Coagulation-Fragmentation Equations , 2000 .

[38]  L. Diósi On High-Temperature Markovian Equation for Quantum Brownian Motion , 1993 .

[39]  Pavel B Dubovskii,et al.  Mathematical theory of coagulation , 1994 .

[40]  O. Penrose,et al.  Towards a rigorous molecular theory of metastability , 1979 .

[41]  Benoît Perthame,et al.  Gelation and mass conservation in coagulation-fragmentation models , 2003 .

[42]  N. Dunford,et al.  Linear operations on summable functions , 1940 .

[43]  John L. Spouge,et al.  An existence theorem for the discrete coagulation–fragmentation equations , 1984, Mathematical Proceedings of the Cambridge Philosophical Society.

[44]  Stéphane Mischler,et al.  Existence globale pour l'équation de Smoluchowski continue non homogène et comportement asymptotique des solutions , 2003 .

[45]  A. A Lushnikov,et al.  Coagulation in finite systems , 1978 .

[46]  I. Lifshitz,et al.  The kinetics of precipitation from supersaturated solid solutions , 1961 .

[47]  Nelson Dunford A mean ergodic theorem , 1939 .

[48]  P. Meyer,et al.  Probabilités et potentiel , 1966 .

[49]  Felix Otto,et al.  Identification of the Dilute Regime in Particle Sedimentation , 2004 .

[50]  J. Carrillo,et al.  Asymptotic Behaviour and Self-Similarity for the Three Dimensional Vlasov–Poisson–Fokker–Planck System , 1996 .

[51]  Decoherent Histories and Quantum State Diffusion , 1994, gr-qc/9403047.

[52]  M. Smoluchowski,et al.  Drei Vortrage uber Diffusion, Brownsche Bewegung und Koagulation von Kolloidteilchen , 1916 .

[53]  J. Dieudonné,et al.  Sur les espaces de Köthe , 1951 .

[54]  Dariusz Wrzosek,et al.  Sol-gel transition in a coagulation-diffusion model , 2000 .

[55]  Miguel A. Herrero,et al.  A note on Smoluchowski's equations with diffusion , 2005, Appl. Math. Lett..

[56]  H. Brezis Analyse fonctionnelle : théorie et applications , 1983 .

[57]  Jack Carr,et al.  The Becker-Döring cluster equations: Basic properties and asymptotic behaviour of solutions , 1986 .

[58]  Jack Carr,et al.  Asymptotic behaviour of solutions to the Becker-Döring equations for arbitrary initial data , 1988, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[59]  S. Mischler,et al.  The Continuous Coagulation-Fragmentation¶Equations with Diffusion , 2002 .

[60]  P. Jabin,et al.  On the rate of convergence to equilibrium in the Becker–Döring equations , 2003 .

[61]  L. Erdős,et al.  Fokker–Planck Equations as Scaling Limits of Reversible Quantum Systems , 2000 .

[62]  Barbara Niethammer,et al.  On the Evolution of Large Clusters in the Becker-Döring Model , 2003, J. Nonlinear Sci..

[63]  P. Laurençot THE DISCRETE COAGULATION EQUATIONS WITH MULTIPLE FRAGMENTATION , 2002, Proceedings of the Edinburgh Mathematical Society.

[64]  Juan Soler,et al.  An Analysis of Quantum Fokker-Planck Models: A Wigner Function Approach , 2004 .

[65]  Michael Grabe,et al.  Protein interactions and membrane geometry. , 2003, Biophysical journal.

[66]  R. Becker,et al.  Kinetische Behandlung der Keimbildung in übersättigten Dämpfen , 1935 .

[67]  Miguel Escobedo Martínez,et al.  Gelation in coagulation and fragmentation models , 2002 .

[68]  William R. Frensley,et al.  Boundary conditions for open quantum systems driven far from equilibrium , 1990 .