Existence of the fundamental solution of a second order evolution equation
Annales Polonici Mathematici (1997)
- Volume: 66, Issue: 1, page 15-35
- ISSN: 0066-2216
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topJan Bochenek. "Existence of the fundamental solution of a second order evolution equation." Annales Polonici Mathematici 66.1 (1997): 15-35. <http://eudml.org/doc/269952>.
@article{JanBochenek1997,
abstract = {We give sufficient conditions for the existence of the fundamental solution of a second order evolution equation. The proof is based on stable approximations of an operator A(t) by a sequence $\{A_n(t)\}$ of bounded operators.},
author = {Jan Bochenek},
journal = {Annales Polonici Mathematici},
keywords = {evolution problem; stable family of operators; stable approximations of the evolution operator; fundamental solution; Cauchy problem; uniformly correct Cauchy problem; fundamental solutions; second-order evolution equations; Cauchy problems},
language = {eng},
number = {1},
pages = {15-35},
title = {Existence of the fundamental solution of a second order evolution equation},
url = {http://eudml.org/doc/269952},
volume = {66},
year = {1997},
}
TY - JOUR
AU - Jan Bochenek
TI - Existence of the fundamental solution of a second order evolution equation
JO - Annales Polonici Mathematici
PY - 1997
VL - 66
IS - 1
SP - 15
EP - 35
AB - We give sufficient conditions for the existence of the fundamental solution of a second order evolution equation. The proof is based on stable approximations of an operator A(t) by a sequence ${A_n(t)}$ of bounded operators.
LA - eng
KW - evolution problem; stable family of operators; stable approximations of the evolution operator; fundamental solution; Cauchy problem; uniformly correct Cauchy problem; fundamental solutions; second-order evolution equations; Cauchy problems
UR - http://eudml.org/doc/269952
ER -
References
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- [2] H. O. Fattorini, Ordinary differential equations in linear topological spaces, I, J. Differential Equations 5 (1968), 72-105. Zbl0175.15101
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- [6] M. Kozak, A fundamental solution of a second-order differential equation in a Banach space, Univ. Iagel. Acta Math. 32 (1995), 275-289. Zbl0855.34073
- [7] S. Krein, Linear Differential Equations in Banach Space, Amer. Math. Soc., 1972.
- [8] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci. 44, Springer, 1983.
- [9] H. Tanabe, Equations of Evolution, Pitman, London, 1979.
- [10] C. C. Travis and G. F. Webb, Cosine families and abstract nonlinear second order differential equations, Acta Math. Acad. Sci. Hungar. 32 (1978), 75-96. Zbl0388.34039
- [11] T. Winiarska, Evolution equations of second order with operator depending on t, in: Selected Problems of Mathematics, Cracow University of Technology, Anniversary issue, 1995, 299-311.
- [12] K. Yosida, Functional Analysis, Springer, New York, 1980.
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