On the initial value problem of a class of models of the kinetic theory for active particles

Applied Mathematics Letters

Volumn 24, Issue 3, 2011, Pages 257-263

  Arlotti, L ^a   De Angelis, E ^b  

^a UNIVERSITY OF UDINE   (Italy)

^b POLITECNICO DI TORINO   (Italy)

Author keywords

Cauchy problem; Evolution equations; Kinetic theory

Indexed keywords

ACTIVE PARTICLES; BIOLOGICAL BEHAVIOR; CAUCHY PROBLEMS; EVOLUTION EQUATIONS; MICROSCOPIC INTERACTION; QUALITATIVE ANALYSIS; SELF ORGANIZING;

INITIAL VALUE PROBLEMS; KINETIC THEORY;

DIFFERENTIAL EQUATIONS;

EID: 78649982880     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2010.09.015     Document Type: Article

References (16)

1. N. Bellomo, C. Bianca, and M. Delitala Complexity analysis and mathematical tools towards the modelling of living systems Phys. Life Rev. 6 2009 144 175
2. N. Bellomo, N.K. Li, and P.K. Maini On the foundation of cancer modeling selected topics, speculations, and perspectives Math. Models Methods Appl. Sci. 18 2008 593 646
3. N. Bellomo, and G. Forni Complex multicellular systems and immune competition: new paradigms looking for a mathematical theory Curr. Top. Dev. Biol. 81 2008 485 502
4. G. Ajmone Marsan On the modelling and simulation of the competition for a secession under media influence by active particles methods and functional subsystems decomposition Comput. Math. Appl. 57 2009 710 728
5. N. Bellomo, and B. Carbonaro On the complexity of multiple interactions with additional reasonings about Kate, Jules and Jim Math. Comput. Modelling 47 2008 168 177
6. G. Ajmone Marsan New paradigms towards the modelling of complex systems in behavioral economics Math. Comput. Modelling 50 2009 584 597
7. L. Arlotti, N. Bellomo, and E. De Angelis Generalized kinetic (Boltzmann) models: mathematical structures and applications Math. Models Methods Appl. Sci. Sci. 12 2002 567 591
8. P.E. Jabin, V. Lemesle, and D. Aurelle A continuous size-structured red coral growth model Math. Models Methods Appl. Sci. 18 2008 1927 1944
9. G. Webb Population models structured by age, size, and spatial position. Structured population models in biology and epidemiology Lecture Notes in Math.1936 2008 Springer Berlin 1 49
10. N. Bellomo, A. Bellouquid, J. Nieto, and J. Soler Complexity and mathematical tools toward the modelling of multicellular growing systems Math. Comput. Modelling 51 2010 441 451
11. N. Bellomo, A. Bellouquid, J. Nieto, and J. Soler Multiscale biological tissue models and flux-limited chemotaxis from binary mixtures of multicellular growing systems Math. Models Methods Appl. Sci. 20 2010 1179 1207
12. S. De Lillo, M. Delitala, and C. Salvatori Modelling epidemics and virus mutations by methods of the mathematical kinetic theory for active particles Math. Models Methods Appl. Sci. 19 suppl. 2009 1405 1425
13. V. Liskevich, H. Vogt, and J. Voigt Gaussian bounds for propagators perturbed by potentials J. Funct. Anal. 238 2006 245 277
14. L. Arlotti, J. Banasiak, Nonautonomous fragmentation equation via evolution semigroups, Math. Methods Appl. Sci., doi:10.1002/mma.1282.
15. D.J. McLaughlin, W. Lamb, and A.C. McBride Existence and uniqueness results for the non-autonomous coagulation and multiple-fragmentation equation Math. Methods Appl. Sci. 21 1998 1067 1084
16. L. Arlotti, N. Bellomo, and K. Latrach From the Jager and Segel model to kinetic population dynamics nonlinear evolution problems and applications Math. Comput. Modelling 30 1999 15 40