Semilinear evolution equations of the parabolic type
Annales Polonici Mathematici (1999)
- Volume: 72, Issue: 3, page 197-206
- ISSN: 0066-2216
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topBochenek, Jan. "Semilinear evolution equations of the parabolic type." Annales Polonici Mathematici 72.3 (1999): 197-206. <http://eudml.org/doc/262706>.
@article{Bochenek1999,
abstract = {This paper is devoted to the investigation of the abstract semilinear initial value problem du/dt + A(t)u = f(t,u), u(0) = u₀, in the "parabolic" case.},
author = {Bochenek, Jan},
journal = {Annales Polonici Mathematici},
keywords = {classical solution; semilinear initial value problem; analytic semigroup; mild solution},
language = {eng},
number = {3},
pages = {197-206},
title = {Semilinear evolution equations of the parabolic type},
url = {http://eudml.org/doc/262706},
volume = {72},
year = {1999},
}
TY - JOUR
AU - Bochenek, Jan
TI - Semilinear evolution equations of the parabolic type
JO - Annales Polonici Mathematici
PY - 1999
VL - 72
IS - 3
SP - 197
EP - 206
AB - This paper is devoted to the investigation of the abstract semilinear initial value problem du/dt + A(t)u = f(t,u), u(0) = u₀, in the "parabolic" case.
LA - eng
KW - classical solution; semilinear initial value problem; analytic semigroup; mild solution
UR - http://eudml.org/doc/262706
ER -
References
top- [1] P. Acquistapace and B. Terreni, On quasilinear parabolic systems, Math. Ann. 282 (1988), 315-335. Zbl0629.34018
- [2] J. Bochenek, An abstract semilinear first order differential equation in the hyperbolic case, Ann. Polon. Math. 61 (1995), 13-23. Zbl0847.34064
- [3] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math. 840, Springer, Berlin, 1981. Zbl0456.35001
- [4] T. Kato, Perturbation Theory of Linear Operators, Grundlehren Math. Wiss. 132, Springer, New York, 1980.
- [5] M. Kozak, An abstract nonlinear temporally inhomogeneous equation, Demonstratio Math. 23 (1990), 993-1003. Zbl0746.34038
- [6] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, 1983.
- [7] H. Tanabe, Equations of Evolution, Pitman, London, 1979.
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