Existence of the fundamental solution of a second order evolution equation
Jan Bochenek
Annales Polonici Mathematici, Tome 66 (1997), p. 15-35 / Harvested from The Polish Digital Mathematics Library

We give sufficient conditions for the existence of the fundamental solution of a second order evolution equation. The proof is based on stable approximations of an operator A(t) by a sequence An(t) of bounded operators.

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:269952
@article{bwmeta1.element.bwnjournal-article-apmv66z1p15bwm,
     author = {Jan Bochenek},
     title = {Existence of the fundamental solution of a second order evolution equation},
     journal = {Annales Polonici Mathematici},
     volume = {66},
     year = {1997},
     pages = {15-35},
     zbl = {0894.34054},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv66z1p15bwm}
}
Jan Bochenek. Existence of the fundamental solution of a second order evolution equation. Annales Polonici Mathematici, Tome 66 (1997) pp. 15-35. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv66z1p15bwm/

[000] [1] J. Bochenek and T. Winiarska, Evolution equations with parameter in the hyperbolic case, Ann. Polon. Math. 64 (1996), 47-60. | Zbl 0855.34070

[001] [2] H. O. Fattorini, Ordinary differential equations in linear topological spaces, I, J. Differential Equations 5 (1968), 72-105. | Zbl 0175.15101

[002] [3] H. O. Fattorini, Ordinary differential equations in linear topological spaces, II, J. Differential Equations 6 (1969), 50-70. | Zbl 0181.42801

[003] [4] H. O. Fattorini, Second Order Linear Differential Equations in Banach Spaces, North-Holland, New York, 1985. | Zbl 0564.34063

[004] [5] T. Kato, Perturbation Theory for Linear Operators, Grundlehren Math. Wiss. 132, Springer, New York, 1980.

[005] [6] M. Kozak, A fundamental solution of a second-order differential equation in a Banach space, Univ. Iagel. Acta Math. 32 (1995), 275-289. | Zbl 0855.34073

[006] [7] S. Krein, Linear Differential Equations in Banach Space, Amer. Math. Soc., 1972.

[007] [8] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci. 44, Springer, 1983.

[008] [9] H. Tanabe, Equations of Evolution, Pitman, London, 1979.

[009] [10] 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

[010] [11] T. Winiarska, Evolution equations of second order with operator depending on t, in: Selected Problems of Mathematics, Cracow University of Technology, Anniversary issue, 1995, 299-311.

[011] [12] K. Yosida, Functional Analysis, Springer, New York, 1980.