# Evolution equations with parameter in the hyperbolic case

Jan Bochenek; Teresa Winiarska

Annales Polonici Mathematici (1996)

- Volume: 64, Issue: 1, page 47-60
- ISSN: 0066-2216

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topJan Bochenek, and Teresa Winiarska. "Evolution equations with parameter in the hyperbolic case." Annales Polonici Mathematici 64.1 (1996): 47-60. <http://eudml.org/doc/269947>.

@article{JanBochenek1996,

abstract = {The purpose of this paper is to give theorems on continuity and differentiability with respect to (h,t) of the solution of the initial value problem du/dt = A(h,t)u + f(h,t), u(0) = u₀(h) with parameter $h ∈ Ω ⊂ ℝ^m$ in the “hyperbolic” case.},

author = {Jan Bochenek, Teresa Winiarska},

journal = {Annales Polonici Mathematici},

keywords = {evolution problem; stable family of operators; stable approximations of the evolution operator; evolution problem with parameter; hyperbolic case; continuity; differentiability; Cauchy problem},

language = {eng},

number = {1},

pages = {47-60},

title = {Evolution equations with parameter in the hyperbolic case},

url = {http://eudml.org/doc/269947},

volume = {64},

year = {1996},

}

TY - JOUR

AU - Jan Bochenek

AU - Teresa Winiarska

TI - Evolution equations with parameter in the hyperbolic case

JO - Annales Polonici Mathematici

PY - 1996

VL - 64

IS - 1

SP - 47

EP - 60

AB - The purpose of this paper is to give theorems on continuity and differentiability with respect to (h,t) of the solution of the initial value problem du/dt = A(h,t)u + f(h,t), u(0) = u₀(h) with parameter $h ∈ Ω ⊂ ℝ^m$ in the “hyperbolic” case.

LA - eng

KW - evolution problem; stable family of operators; stable approximations of the evolution operator; evolution problem with parameter; hyperbolic case; continuity; differentiability; Cauchy problem

UR - http://eudml.org/doc/269947

ER -

## References

top- [1] T. Kato, Perturbation Theory for Linear Operators, Springer, 1980. Zbl0435.47001
- [2] S. G. Krein, Linear Differential Equations in Banach Space, Transl. Amer. Math. Soc. 29, Providence, R.I., 1971.
- [3] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, 1983.
- [4] H. Tanabe, Equations of Evolution, Pitman, 1979.
- [5] T. Winiarska, Parabolic equations with coefficients depending on t and parameters, Ann. Polon. Math. 51 (1990), 325-339. Zbl0738.35020
- [6] T. Winiarska, Regularity of solutions of parabolic equations with coefficients depending on t and parameters, Ann. Polon. Math. 56 (1992), 311-317. Zbl0763.35015

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