Evolution semigroups for nonautonomous Cauchy problems
Nickel, Gregor
Abstr. Appl. Anal., Tome 2 (1997) no. 1-2, p. 73-95 / Harvested from Project Euclid
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In this paper, we characterize wellposedness of nonautonomous, linear Cauchy problems $$(NCP)\begin{cases}\dot{u}(t) = A(t)u(t)\\ u(s) = x\in X \end{cases}$$ on a Banach space $X$ by the existence of certain evolution semigroups. ¶ Then, we use these generation results for evolution semigroups to derive wellposedness for nonautonomous Cauchy problems under some “concrete” conditions. As a typical example, we discuss the so called “parabolic” case.
Publié le : 1997-05-14
Classification:  Evolution semigroup,  nonautonomous abstract Cauchy problem,  perturbation theory,  parabolic problems,  47D06,  47A55 
@article{1049737244,
     author = {Nickel, Gregor},
     title = {Evolution semigroups for nonautonomous Cauchy problems},
     journal = {Abstr. Appl. Anal.},
     volume = {2},
     number = {1-2},
     year = {1997},
     pages = { 73-95},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1049737244}
}

Nickel, Gregor. Evolution semigroups for nonautonomous Cauchy problems. Abstr. Appl. Anal., Tome 2 (1997) no. 1-2, pp.  73-95. http://gdmltest.u-ga.fr/item/1049737244/