# Generalized telegraph equation and the Sova-Kurtz version of the Trotter-Kato theorem

Annales Polonici Mathematici (1996)

- Volume: 64, Issue: 1, page 37-45
- ISSN: 0066-2216

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topAdam Bobrowski. "Generalized telegraph equation and the Sova-Kurtz version of the Trotter-Kato theorem." Annales Polonici Mathematici 64.1 (1996): 37-45. <http://eudml.org/doc/269996>.

@article{AdamBobrowski1996,

abstract = {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.},

author = {Adam Bobrowski},

journal = {Annales Polonici Mathematici},

keywords = {telegraph equation; Trotter-Kato theorem; extended limit of operators; Sova-Kurtz approximation theorem; semigroups; telegraph equation with small parameter; diffusion equation with varying boundary conditions},

language = {eng},

number = {1},

pages = {37-45},

title = {Generalized telegraph equation and the Sova-Kurtz version of the Trotter-Kato theorem},

url = {http://eudml.org/doc/269996},

volume = {64},

year = {1996},

}

TY - JOUR

AU - Adam Bobrowski

TI - Generalized telegraph equation and the Sova-Kurtz version of the Trotter-Kato theorem

JO - Annales Polonici Mathematici

PY - 1996

VL - 64

IS - 1

SP - 37

EP - 45

AB - 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.

LA - eng

KW - telegraph equation; Trotter-Kato theorem; extended limit of operators; Sova-Kurtz approximation theorem; semigroups; telegraph equation with small parameter; diffusion equation with varying boundary conditions

UR - http://eudml.org/doc/269996

ER -

## References

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- [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. Zbl0232.47045
- [11] T. G. Kurtz, Extensions of Trotter's operator semigroup approximation theorems, J. Funct. Anal. 3 (1969), 354-375. Zbl0174.18401
- [12] R. S. Phillips, Perturbation theory for semi-groups of operators, Trans. Amer. Math. Soc. 74 (1953), 199-221.
- [13] M. Sova, Cosine operator functions, Dissertationes Math. 49 (1966).
- [14] M. Sova, Convergence d'opérations linéaires non bornées, Rev. Roumaine Math. Pures Appl. 12 (1967), 373-389. Zbl0147.34201
- [15] H. F. Trotter, Approximation of semi-groups of operators, Pacific J. Math. 8 (1958), 887-919. Zbl0099.10302
- [16] K. Yosida, Functional Analysis, Springer, Berlin, 1968.

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