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

Abstract

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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.

How to cite

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Jan 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

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