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

Adam Bobrowski

Annales Polonici Mathematici (1996)

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

Abstract

top
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.

How to cite

top

Adam 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

top
  1. [1] A. Bobrowski, Degenerate convergence of semigroups, Semigroup Forum 49 (1994), 303-327. Zbl0817.47047
  2. [2] A. Bobrowski, Examples of pointwise convergence of semigroups, Ann. Univ. Mariae Curie-Skłodowska Sect. A 49 (1995), to appear. 
  3. [3] E. B. Davies, One-Parameter Semigroups, Academic Press, London, 1980. Zbl0457.47030
  4. [4] S. N. Ethier and T. G. Kurtz, Markov Processes. Characterization and Convergence, Wiley Ser. Probab. Math. Statist., Wiley, New York, 1986. 
  5. [5] H. O. Fattorini, Ordinary differential equations in topological vector spaces I, J. Differential Equations 5 (1969), 72-105. Zbl0175.15101
  6. [6] H. O. Fattorini, Ordinary differential equations in topological vector spaces II, J. Differential Equations 6 (1969), 50-70. Zbl0181.42801
  7. [7] H. O. Fattorini, The hyperbolic singular perturbation problem: an operator theoretic approach, J. Differential Equations 70 (1987), 1-41. Zbl0633.35006
  8. [8] J. A. Goldstein, Semigroups of Linear Operators and Applications, Oxford Math. Monographs, Oxford Univ. Press, 1985. Zbl0592.47034
  9. [9] J. Kisyński, On cosine operator functions and one-parameter groups of operators, Studia Math. 44 (1972), 93-105. Zbl0232.47045
  10. [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. [11] T. G. Kurtz, Extensions of Trotter's operator semigroup approximation theorems, J. Funct. Anal. 3 (1969), 354-375. Zbl0174.18401
  12. [12] R. S. Phillips, Perturbation theory for semi-groups of operators, Trans. Amer. Math. Soc. 74 (1953), 199-221. 
  13. [13] M. Sova, Cosine operator functions, Dissertationes Math. 49 (1966). 
  14. [14] M. Sova, Convergence d'opérations linéaires non bornées, Rev. Roumaine Math. Pures Appl. 12 (1967), 373-389. Zbl0147.34201
  15. [15] H. F. Trotter, Approximation of semi-groups of operators, Pacific J. Math. 8 (1958), 887-919. Zbl0099.10302
  16. [16] K. Yosida, Functional Analysis, Springer, Berlin, 1968. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.