Nonlinear semigroups and the existence and stability of solutions
of semilinear nonautonomous evolution equations

Aulbach, Bernd; Minh, Nguyen Van

Nonlinear semigroups and the existence and stability of solutions of semilinear nonautonomous evolution equations

Abstr. Appl. Anal., Tome 1 (1996) no. 1, p. 351-380 / Harvested from Project Euclid

Résumé

This paper is concerned with the existence and stability of solutions of a class of semilinear nonautonomous evolution equations. A procedure is discussed which associates to each nonautonomous equation the so-called evolution semigroup of (possibly nonlinear) operators. Sufficient conditions for the existence and stability of solutions and the existence of periodic oscillations are given in terms of the accretiveness of the corresponding infinitesimal generator. Furthermore, through the existence of integral manifolds for abstract evolutionary processes we obtain a reduction principle for stability questions of mild solutions. The results are applied to a class of partial functional differential equations.

Publié le : 1996-05-14
Classification: Evolutionary process, evolution semigroup, semilinear nonautonomous equation, nonlinear semigroup, stability, periodic solution, accretive operator, integral manifold, instability, 34G20, 34K30, 47H20

@article{1049726080,
     author = {Aulbach, Bernd and Minh, Nguyen Van},
     title = {Nonlinear semigroups and the existence and stability of solutions
of semilinear nonautonomous evolution equations},
     journal = {Abstr. Appl. Anal.},
     volume = {1},
     number = {1},
     year = {1996},
     pages = { 351-380},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1049726080}
}

Aulbach, Bernd; Minh, Nguyen Van. Nonlinear semigroups and the existence and stability of solutions
of semilinear nonautonomous evolution equations. Abstr. Appl. Anal., Tome 1 (1996) no. 1, pp.  351-380. http://gdmltest.u-ga.fr/item/1049726080/