Second order evolution equations with parameter
Jan Bochenek ; Teresa Winiarska
Annales Polonici Mathematici, Tome 60 (1994), p. 41-52 / Harvested from The Polish Digital Mathematics Library

We give some theorems on continuity and differentiability with respect to (h,t) of the solution of a second order evolution problem with parameter hΩm. Our main tool is the theory of strongly continuous cosine families of linear operators in Banach spaces.

Publié le : 1994-01-01
EUDML-ID : urn:eudml:doc:262479
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     author = {Jan Bochenek and Teresa Winiarska},
     title = {Second order evolution equations with parameter},
     journal = {Annales Polonici Mathematici},
     volume = {60},
     year = {1994},
     pages = {41-52},
     zbl = {0798.34082},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv59z1p41bwm}
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Jan Bochenek; Teresa Winiarska. Second order evolution equations with parameter. Annales Polonici Mathematici, Tome 60 (1994) pp. 41-52. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv59z1p41bwm/

[000] [1] J. Bochenek, An abstract nonlinear second order differential equation, Ann. Polon. Math. 54 (1991), 155-166. | Zbl 0724.34069

[001] [2] H. O. Fattorini, Ordinary differential equations in linear topological spaces, I, J. Differential Equations 15 (1968), 72-105. | Zbl 0175.15101

[002] [3] T. Kato, Perturbation Theory for Linear Operators, Springer, New York, 1980.

[003] [4] S. Krein, Linear Differential Equations in Banach Space, Amer. Math. Soc., 1972.

[004] [5] M. Schechter, Differentiability of solutions of elliptic problems with respect to parameters, Boll. Un. Mat. Ital. A (5) 13 (1976), 601-608. | Zbl 0352.35042

[005] [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. | Zbl 0388.34039

[006] [7] T. Winiarska, Evolution equation with parameter, Univ. Iagell. Acta Math. 28 (1987), 219-227. | Zbl 0673.47035

[007] [8] T. Winiarska, Differential Equations with Parameter, Monograph 68, T. Kościuszko Technical Univ. of Cracow, 1988.

[008] [9] T. Winiarska, Parabolic equations with coefficients depending on t and parameters, Ann. Polon. Math. 51 (1990), 325-339. | Zbl 0738.35020