Evolution equations with parameter in the hyperbolic case

• Autorzy: Jan Bochenek , Teresa Winiarska
• Języki publikacji: EN

Abstrakty

EN

The purpose of this paper is to give theorems on continuity and differentiability with respect to (h,t) of the solution of the initial value problem du/dt = A(h,t)u + f(h,t), u(0) = u₀(h) with parameter $h ∈ Ω ⊂ ℝ^m$ in the "hyperbolic" case.

Słowa kluczowe

EN

evolution problem; stable family of operators; stable approximations of the evolution operator; evolution problem with parameter; hyperbolic case

Kategorie tematyczne

• 34K30: Equations in abstract spaces
• 35B30: Dependence of solutions on initial and boundary data, parameters

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996
• Tom: 64
• Numer: 1
• Strony: 47-60

Daty

wydano

1996

otrzymano

1994-12-08

poprawiono

1995-04-27

Twórcy

autor

Jan Bochenek

• Institute of Mathematics, Technical University of Kraków, Warszawska 24, 31-155 Kraków, Poland

autor

Teresa Winiarska

• Institute of Mathematics, Technical University of Kraków, Warszawska 24, 31-155 Kraków, Poland

Bibliografia

• [1] T. Kato, Perturbation Theory for Linear Operators, Springer, 1980.
• [2] S. G. Krein, Linear Differential Equations in Banach Space, Transl. Amer. Math. Soc. 29, Providence, R.I., 1971.
• [3] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, 1983.
• [4] H. Tanabe, Equations of Evolution, Pitman, 1979.
• [5] T. Winiarska, Parabolic equations with coefficients depending on t and parameters, Ann. Polon. Math. 51 (1990), 325-339.
• [6] T. Winiarska, Regularity of solutions of parabolic equations with coefficients depending on t and parameters, Ann. Polon. Math. 56 (1992), 311-317.