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1997 | 66 | 1 | 15-35
Tytuł artykułu

Existence of the fundamental solution of a second order evolution equation

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Abstrakty
EN
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 ${A_n(t)}$ of bounded operators.
Twórcy
autor
  • Institute of Mathematics, Technical University of Kraków, Warszawska 24, 31-155 Kraków, Poland
Bibliografia
  • [1] J. Bochenek and T. Winiarska, Evolution equations with parameter in the hyperbolic case, Ann. Polon. Math. 64 (1996), 47-60.
  • [2] H. O. Fattorini, Ordinary differential equations in linear topological spaces, I, J. Differential Equations 5 (1968), 72-105.
  • [3] H. O. Fattorini, Ordinary differential equations in linear topological spaces, II, J. Differential Equations 6 (1969), 50-70.
  • [4] H. O. Fattorini, Second Order Linear Differential Equations in Banach Spaces, North-Holland, New York, 1985.
  • [5] T. Kato, Perturbation Theory for Linear Operators, Grundlehren Math. Wiss. 132, Springer, New York, 1980.
  • [6] M. Kozak, A fundamental solution of a second-order differential equation in a Banach space, Univ. Iagel. Acta Math. 32 (1995), 275-289.
  • [7] S. Krein, Linear Differential Equations in Banach Space, Amer. Math. Soc., 1972.
  • [8] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci. 44, Springer, 1983.
  • [9] H. Tanabe, Equations of Evolution, Pitman, London, 1979.
  • [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.
  • [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.
  • [12] K. Yosida, Functional Analysis, Springer, New York, 1980.
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Bibliografia
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bwmeta1.element.bwnjournal-article-apmv66z1p15bwm
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