Second order evolution equations with parameter

Jan Bochenek; Teresa Winiarska

Annales Polonici Mathematici (1994)

  • Volume: 59, Issue: 1, page 41-52
  • ISSN: 0066-2216

Abstract

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We give some theorems on continuity and differentiability with respect to (h,t) of the solution of a second order evolution problem with parameter h ∈ Ω ⊂ ℝ m . Our main tool is the theory of strongly continuous cosine families of linear operators in Banach spaces.

How to cite

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Jan Bochenek, and Teresa Winiarska. "Second order evolution equations with parameter." Annales Polonici Mathematici 59.1 (1994): 41-52. <http://eudml.org/doc/262479>.

@article{JanBochenek1994,
abstract = {We give some theorems on continuity and differentiability with respect to (h,t) of the solution of a second order evolution problem with parameter $h ∈ Ω ⊂ ℝ^m$. Our main tool is the theory of strongly continuous cosine families of linear operators in Banach spaces.},
author = {Jan Bochenek, Teresa Winiarska},
journal = {Annales Polonici Mathematici},
keywords = {evolution problem; cosine family; evolution problem with parameter; continuity; differentiability; second order evolution equation; Banach space},
language = {eng},
number = {1},
pages = {41-52},
title = {Second order evolution equations with parameter},
url = {http://eudml.org/doc/262479},
volume = {59},
year = {1994},
}

TY - JOUR
AU - Jan Bochenek
AU - Teresa Winiarska
TI - Second order evolution equations with parameter
JO - Annales Polonici Mathematici
PY - 1994
VL - 59
IS - 1
SP - 41
EP - 52
AB - We give some theorems on continuity and differentiability with respect to (h,t) of the solution of a second order evolution problem with parameter $h ∈ Ω ⊂ ℝ^m$. Our main tool is the theory of strongly continuous cosine families of linear operators in Banach spaces.
LA - eng
KW - evolution problem; cosine family; evolution problem with parameter; continuity; differentiability; second order evolution equation; Banach space
UR - http://eudml.org/doc/262479
ER -

References

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  1. [1] J. Bochenek, An abstract nonlinear second order differential equation, Ann. Polon. Math. 54 (1991), 155-166. Zbl0724.34069
  2. [2] H. O. Fattorini, Ordinary differential equations in linear topological spaces, I, J. Differential Equations 15 (1968), 72-105. Zbl0175.15101
  3. [3] T. Kato, Perturbation Theory for Linear Operators, Springer, New York, 1980. 
  4. [4] S. Krein, Linear Differential Equations in Banach Space, Amer. Math. Soc., 1972. 
  5. [5] M. Schechter, Differentiability of solutions of elliptic problems with respect to parameters, Boll. Un. Mat. Ital. A (5) 13 (1976), 601-608. Zbl0352.35042
  6. [6] 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
  7. [7] T. Winiarska, Evolution equation with parameter, Univ. Iagell. Acta Math. 28 (1987), 219-227. Zbl0673.47035
  8. [8] T. Winiarska, Differential Equations with Parameter, Monograph 68, T. Kościuszko Technical Univ. of Cracow, 1988. 
  9. [9] T. Winiarska, Parabolic equations with coefficients depending on t and parameters, Ann. Polon. Math. 51 (1990), 325-339. Zbl0738.35020

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