On self-similarity and stationary problem for fragmentation and coagulation models
M. Escobedo, S. Mischler, M. Rodriguez Ricard (2005)
Annales de l'I.H.P. Analyse non linéaire
Tran Duc Van, Le Van Hap, Nguyen Duy Thai Son (1998)
Journal of Inequalities and Applications [electronic only]
Aldo Andreotti, Gregory Fredricks, Mauro Nacinovich (1981)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Antoni Leon Dawidowicz, Anna Poskrobko, Jerzy Leszek Zalasiński (2011)
Applicationes Mathematicae
The paper deals with the description of a model which is the synthesis of two classical models, the Lotka-Volterra and McKendrick-von Foerster models. The existence and uniqueness of the solution for the new population problem are proved, as well the asymptotic periodicity but under some simplifying assumptions.
Z. Kamont (1977)
Annales Polonici Mathematici
W. Mlak, E. Schechter (1969)
Annales Polonici Mathematici
Z. Kamont (1980)
Annales Polonici Mathematici
Z. Kamont, W. Pawelski (1974)
Annales Polonici Mathematici
Dawidowicz, Antoni Leon, Haribash, Najemedin (2005)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
François Golse, Bernt Wennberg (2000)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
François Golse, Bernt Wennberg (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
Consider the domain and let the free path length be defined as In the Boltzmann-Grad scaling corresponding to , it is shown that the limiting distribution of is bounded from below by an expression of the form C/t, for some C> 0. A numerical study seems to indicate that asymptotically for large t, . This is an extension of a previous work [J. Bourgain et al., Comm. Math. Phys.190 (1998) 491-508]. As a consequence, it is proved that the linear Boltzmann type transport equation is inappropriate...
C. Bardos, Kuo Pen Yu (1983)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Antoni Leon Dawidowicz (1983)
Annales Polonici Mathematici
Tomasz Człapiński (1991)
Czechoslovak Mathematical Journal
Joji Kajiwara, Yasuko Mori (1974)
Czechoslovak Mathematical Journal
Simone Bertone, Arrigo Cellina (2007)
ESAIM: Control, Optimisation and Calculus of Variations
We propose a necessary and sufficient condition about the existence of variations, i.e., of non trivial solutions to the differential inclusion .
Vladislav A. Panferov (2004)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
The Povzner equation is a version of the nonlinear Boltzmann equation, in which the collision operator is mollified in the space variable. The existence of stationary solutions in is established for a class of stationary boundary-value problems in bounded domains with smooth boundaries, without convexity assumptions. The results are obtained for a general type of collision kernels with angular cutoff. Boundary conditions of the diffuse reflection type, as well as the given incoming profile, are...
R Alexandre, C Villani (2004)
Annales de l'I.H.P. Analyse non linéaire
Bernstein, Swanhild (1996)
Bulletin of the Belgian Mathematical Society - Simon Stevin
Tahar-Zamène Boulmezaoud, Yvon Maday, Tahar Amari (1999)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique