The Sova-Kurtz approximation theorem for semigroups is applied to prove convergence of solutions of the telegraph equation with small parameter. Convergence of the solutions of the diffusion equation with varying boundary conditions is also considered.
@article{bwmeta1.element.bwnjournal-article-apmv64z1p37bwm,
author = {Adam Bobrowski},
title = {Generalized telegraph equation and the Sova-Kurtz version of the Trotter-Kato theorem},
journal = {Annales Polonici Mathematici},
volume = {63},
year = {1996},
pages = {37-45},
zbl = {0862.47021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv64z1p37bwm}
}
Adam Bobrowski. Generalized telegraph equation and the Sova-Kurtz version of the Trotter-Kato theorem. Annales Polonici Mathematici, Tome 63 (1996) pp. 37-45. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv64z1p37bwm/
[000] [1] A. Bobrowski, Degenerate convergence of semigroups, Semigroup Forum 49 (1994), 303-327. | Zbl 0817.47047
[001] [2] A. Bobrowski, Examples of pointwise convergence of semigroups, Ann. Univ. Mariae Curie-Skłodowska Sect. A 49 (1995), to appear.
[002] [3] E. B. Davies, One-Parameter Semigroups, Academic Press, London, 1980. | Zbl 0457.47030
[003] [4] S. N. Ethier and T. G. Kurtz, Markov Processes. Characterization and Convergence, Wiley Ser. Probab. Math. Statist., Wiley, New York, 1986.
[004] [5] H. O. Fattorini, Ordinary differential equations in topological vector spaces I, J. Differential Equations 5 (1969), 72-105. | Zbl 0175.15101
[005] [6] H. O. Fattorini, Ordinary differential equations in topological vector spaces II, J. Differential Equations 6 (1969), 50-70. | Zbl 0181.42801
[006] [7] H. O. Fattorini, The hyperbolic singular perturbation problem: an operator theoretic approach, J. Differential Equations 70 (1987), 1-41. | Zbl 0633.35006
[007] [8] J. A. Goldstein, Semigroups of Linear Operators and Applications, Oxford Math. Monographs, Oxford Univ. Press, 1985. | Zbl 0592.47034
[008] [9] J. Kisyński, On cosine operator functions and one-parameter groups of operators, Studia Math. 44 (1972), 93-105. | Zbl 0232.47045
[009] [10] J. Kisyński, On the connection between cosine operator functions and one parameter semi-groups and groups of operators, Wydawnictwo U.W., 1972, 1-9. | Zbl 0232.47045
[010] [11] T. G. Kurtz, Extensions of Trotter's operator semigroup approximation theorems, J. Funct. Anal. 3 (1969), 354-375. | Zbl 0174.18401
[011] [12] R. S. Phillips, Perturbation theory for semi-groups of operators, Trans. Amer. Math. Soc. 74 (1953), 199-221.
[012] [13] M. Sova, Cosine operator functions, Dissertationes Math. 49 (1966).
[013] [14] M. Sova, Convergence d'opérations linéaires non bornées, Rev. Roumaine Math. Pures Appl. 12 (1967), 373-389. | Zbl 0147.34201
[014] [15] H. F. Trotter, Approximation of semi-groups of operators, Pacific J. Math. 8 (1958), 887-919. | Zbl 0099.10302
[015] [16] K. Yosida, Functional Analysis, Springer, Berlin, 1968.