# Second order evolution equations with parameter

Jan Bochenek; Teresa Winiarska

Annales Polonici Mathematici (1994)

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

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topJan 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

top- [1] J. Bochenek, An abstract nonlinear second order differential equation, Ann. Polon. Math. 54 (1991), 155-166. Zbl0724.34069
- [2] H. O. Fattorini, Ordinary differential equations in linear topological spaces, I, J. Differential Equations 15 (1968), 72-105. Zbl0175.15101
- [3] T. Kato, Perturbation Theory for Linear Operators, Springer, New York, 1980.
- [4] S. Krein, Linear Differential Equations in Banach Space, Amer. Math. Soc., 1972.
- [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] 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] T. Winiarska, Evolution equation with parameter, Univ. Iagell. Acta Math. 28 (1987), 219-227. Zbl0673.47035
- [8] T. Winiarska, Differential Equations with Parameter, Monograph 68, T. Kościuszko Technical Univ. of Cracow, 1988.
- [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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