Abstract
By a direct investigation on the higher order abstract Cauchy problem. u (n) (t)+ \(\sum {_{i = 0}^{n - 1} \mathop A\nolimits_i \mathop u\nolimits^{(i)} (t) = 0} \) (t≥0);u (k) (0)=u k ,(0≤k≤n-1), some new results concerning the existence, uniqueness and continuous dependence (in some sense) on the initial data of its solutions are obtained; in the case of n = 2, we improve the corresponding results by Neubrander [5], where the second order problem is reduced to a first order system, and techniques from the theory of “integrated semigroups” are employed. In addition, we carry out a further study on the special case when −An-2 generates an “integrated cosine family ” and A n-1 = 0, D(A i) ⊃ D(A n-2), (0 ≤ i ≤ n-2).
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© 1996 Kluwer Academic Publishers
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Xiao, T., Liang, J. (1996). Integrated Semigroups, Cosine Families and Higher Order Abstract Cauchy Problems. In: Li, B., Wang, S., Yan, S., Yang, CC. (eds) Functional Analysis in China. Mathematics and Its Applications, vol 356. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0185-8_30
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DOI: https://doi.org/10.1007/978-94-009-0185-8_30
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6567-2
Online ISBN: 978-94-009-0185-8
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