Singularly perturbed linear and semilinear hyperbolic systems: Kinetic theory approach to some folk's theorems

Acta Applicandae Mathematicae

Volumn 49, Issue 2, 1997, Pages 199-228

  Banasiak, J ^a  

^a UNIVERSITY OF KWAZULU NATAL   (South Africa)

Author keywords

Asymptotic expansion; Damped wave equation; Hyperbolic systems; Singular perturbations

Indexed keywords

EID: 25444457489     PISSN: 01678019     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1005882912151     Document Type: Article

References (25)

1. Banasiak, J.: Diffusion approximation for the linear Boltzmann equation of semiconductor theory with analysis of the initial layer, J. Math. Anal. Appl. 205 (1997), 216-238.
2. Banasiak, J.: Asymptotic analysis of the linear Boltzmann equation with and without an external field: comparison of various approaches, Transport Theory Statist. Phys. 26(1-2) (1997), 103-119.
3. Banasiak, J. and Mika, J. R.: Asymptotic analysis of the Fokker-Planck equation of Brownian motion, Math. Models Methods Appl. Sci. 4(1) (1994), 17-33.
4. Banasiak, J. and Mika, J. R.: Diffusion limit for the linear Boltzmann equation of the neutron transport theory, Math. Methods Appl. Sci. 17 (1994), 1071-1087.
5. Banasiak, J. and Mika, J. R.: Singularly perturbed telegraph equations with applications in the random walk theory, J. Appl. Math. Stochastic. Anal., to appear.
6. DeFacio, B.: Heat conduction with finite signal speed, J. Math. Phys. 16, 971-980.
7. Frosali, G.: Asymptotic Analysis for a Particle Transport in a Moving Medium, IMA J. Appl. Math., to appear.
8. Frosali, G. and Totaro, S.: A scaled nonlinear mathematical model for interactions of algae with light: existence and uniqueness results, Transport Theory Statist. Phys. 26(1-2), (1997).
9. Goldstein, J. E.: Semigroups of Linear Operators and Applications, Oxford University Press, New York, 1985.
10. Hale, J. K. and Raugel, G.: Upper semicontinuity of the attractor for a singularly perturbed hyperbolic equation, J. Differential Equations 73 (1989), 197-214.
11. Hale, J. K. and Raugel, G.: Lower semicontinuity of the attractor for a singularly perturbed hyperbolic equation, J. Dynamics Differential Equations 2(1) (1990), 19-67.
12. Janssen, A.: The distance between the Kac process and the Wiener process with applications to generalized telegraph equations, J. Theoret. Probab. 3(2), 1990, 349-360.
13. Joseph, D. D. and Preziosi, L.: Heat waves, Rev. Modern Phys. 61(1), 1989, 41-73.
14. Kac, M.: A stochastic model related to the telegrapher's equation, Rocky Mountain J. Math. 4, 1974, 497-509.
15. Mika, J. R.: New asymptotic expansion algorithm for singularly perturbed evolution equations, Math. Methods Appl. Sci. 3 (1981), 172-188.
16. Mika, J. R. and Banasiak, J.: Singularly Perturbed Evolution Equations with Applications to Kinetic Theory, World Scientific, Singapore, 1995.
17. Mika, J. R. and Banasiak, J.: Asymptotic analysis of a model kinetic equation, Math. Models Methods Appl. Sci. 5(7) (1995), 867-885.
18. 1 and diffusion equations, Transport Theory Statist. Phys. 7 (3) (1978), 81-101.
19. Mika, J. R. and Stankiewicz, R.: Asymptotic relationship between telegraphic and diffusion equations, Math. Methods Appl. Sci. 3 (1981), 21-37.
20. Mora, X. and Solá-Morales, J.: The singular limit dynamics of semilinear damped wave equations, J. Differential Equations 78 (1989), 262-307.
21. Palczewski, A.: Exact and Chapman-Enskog solutions for the Carleman model, Math. Methods Appl. Sci. 6 (1984), 417-432.
22. Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
23. Ringeisen, E. and Sentis, R.: On the diffusion approximation of a transport process without time scaling, Asymptotic Anal. 5 (1991), 145-159.
24. Schoene, A.: Semi-groups and a class of singular perturbation problems, Indiana Univ. Math. J. 20 (1970), 247-263.
25. Zauderer, E.: Partial Differential Equations of Applied Mathematics, 2nd edn., Wiley, New York, 1988.