Regularity of solutions of parabolic equations with coefficients depending on t and parameters

T. Winiarska

Annales Polonici Mathematici (1992)

  • Volume: 56, Issue: 3, page 311-317
  • ISSN: 0066-2216

Abstract

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The main object of this paper is to study the regularity with respect to the parameter h of solutions of the problem d u / d t + A h ( t ) u ( t ) = f h ( t ) , u ( 0 ) = u h 0 . The continuity of u with respect to both h and t has been considered in [6].

How to cite

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T. Winiarska. "Regularity of solutions of parabolic equations with coefficients depending on t and parameters." Annales Polonici Mathematici 56.3 (1992): 311-317. <http://eudml.org/doc/262470>.

@article{T1992,
abstract = {The main object of this paper is to study the regularity with respect to the parameter h of solutions of the problem $du/dt + A_h(t)u(t) = f_h(t)$, $u(0)=u_h^0$. The continuity of u with respect to both h and t has been considered in [6].},
author = {T. Winiarska},
journal = {Annales Polonici Mathematici},
language = {eng},
number = {3},
pages = {311-317},
title = {Regularity of solutions of parabolic equations with coefficients depending on t and parameters},
url = {http://eudml.org/doc/262470},
volume = {56},
year = {1992},
}

TY - JOUR
AU - T. Winiarska
TI - Regularity of solutions of parabolic equations with coefficients depending on t and parameters
JO - Annales Polonici Mathematici
PY - 1992
VL - 56
IS - 3
SP - 311
EP - 317
AB - The main object of this paper is to study the regularity with respect to the parameter h of solutions of the problem $du/dt + A_h(t)u(t) = f_h(t)$, $u(0)=u_h^0$. The continuity of u with respect to both h and t has been considered in [6].
LA - eng
UR - http://eudml.org/doc/262470
ER -

References

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  1. [1] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer, 1981. Zbl0456.35001
  2. [2] T. Kato, Perturbation Theory for Linear Operators, Springer, 1966. Zbl0148.12601
  3. [3] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, 1983. 
  4. [4] P. E. Sobolevskiĭ, On equations of parabolic type in a Banach space, Trudy Moskov. Mat. Obshch. 10 (1986), 297-350 (in Russian). 
  5. [5] H. Tanabe, Equations of Evolution, Pitman, 1979. 
  6. [6] T. Winiarska, Parabolic equations with coefficients depending on t and parameters, Ann. Polon. Math. 51 (1990), 325-339. Zbl0738.35020
  7. [7] T. Winiarska, Evolution equation with parameter, Univ. Iag. Acta Math. 28 (1987), 219-227. Zbl0673.47035
  8. [8] T. Winiarska, Differential Equations with Parameters, Monograph 68, Technical University of Cracow, 1988. 
  9. [9] K. Yosida, Functional Analysis, Springer, 1980. 

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