An abstract semilinear first order differential equation in the hyperbolic case

ArticleOriginal scientific text

Title

Authors ¹

Institute of Mathematics, Cracow University of Technology, Warszawska 24, 31-155 Kraków, Poland

This paper is devoted to the investigation of the abstract semilinear initial value problem

d \frac{u}{d t} = A (t) u + f (t, u), u (0) = u_{0}

, in the "hyperbolic" case.

semilinear initial value problem, stable family of operators, hyperbolic case

J. Bochenek, An abstract nonlinear second order differential equation, Ann. Polon. Math. 54 (1991), 155-166.
J. Dugundji and A. Granas, Fixed Point Theory, Vol. I, PWN, Warszawa, 1982.
M. Kozak, An abstract nonlinear temporally inhomogeneous equation, Demonstratio Math. 23 (1990), 993-1003.
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, 1983.
H. Tanabe, Equations of Evolution, Pitman, London, 1979.
T. Winiarska, Differential Equations with Parameter, Monograf. 68, Technical University of Cracow, 1988.