An abstract semilinear first order differential equation in the hyperbolic case

Jan Bochenek

Annales Polonici Mathematici (1995)

  • Volume: 61, Issue: 1, page 13-23
  • ISSN: 0066-2216

Abstract

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This paper is devoted to the investigation of the abstract semilinear initial value problem     d u / d t = A ( t ) u + f ( t , u ) , u ( 0 ) = u 0 , in the “hyperbolic” case.

How to cite

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Jan Bochenek. "An abstract semilinear first order differential equation in the hyperbolic case." Annales Polonici Mathematici 61.1 (1995): 13-23. <http://eudml.org/doc/262427>.

@article{JanBochenek1995,
abstract = {This paper is devoted to the investigation of the abstract semilinear initial value problem     $du/dt = A(t)u + f(t,u), u(0) = u_0$, in the “hyperbolic” case.},
author = {Jan Bochenek},
journal = {Annales Polonici Mathematici},
keywords = {semilinear initial value problem; stable family of operators; hyperbolic case; Banach space; existence and uniqueness theorem},
language = {eng},
number = {1},
pages = {13-23},
title = {An abstract semilinear first order differential equation in the hyperbolic case},
url = {http://eudml.org/doc/262427},
volume = {61},
year = {1995},
}

TY - JOUR
AU - Jan Bochenek
TI - An abstract semilinear first order differential equation in the hyperbolic case
JO - Annales Polonici Mathematici
PY - 1995
VL - 61
IS - 1
SP - 13
EP - 23
AB - This paper is devoted to the investigation of the abstract semilinear initial value problem     $du/dt = A(t)u + f(t,u), u(0) = u_0$, in the “hyperbolic” case.
LA - eng
KW - semilinear initial value problem; stable family of operators; hyperbolic case; Banach space; existence and uniqueness theorem
UR - http://eudml.org/doc/262427
ER -

References

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  1. [1] J. Bochenek, An abstract nonlinear second order differential equation, Ann. Polon. Math. 54 (1991), 155-166. Zbl0724.34069
  2. [2] J. Dugundji and A. Granas, Fixed Point Theory, Vol. I, PWN, Warszawa, 1982. 
  3. [3] M. Kozak, An abstract nonlinear temporally inhomogeneous equation, Demonstratio Math. 23 (1990), 993-1003. Zbl0746.34038
  4. [4] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, 1983. 
  5. [5] H. Tanabe, Equations of Evolution, Pitman, London, 1979. 
  6. [6] T. Winiarska, Differential Equations with Parameter, Monograf. 68, Technical University of Cracow, 1988. 

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