C-Semigroups and the Cauchy Problem
โ Scribed by R. Delaubenfels
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 566 KB
- Volume
- 111
- Category
- Article
- ISSN
- 0022-1236
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๐ SIMILAR VOLUMES
In this paper, we study nonautonomous Cauchy problems for a family of linear operators (A(t)) tโI on some Banach space X by means of evolution semigroups. In particular, we characterize "stability" in the so called "hyperbolic case" on the level of evolution semigroups and derive a product formula
If A is the generator of an exponentially bounded C-cosine function on a ลฝ . Banach space X, then the abstract Cauchy problem ACP for A has a unique ลฝ . ลฝ . y 1 ลฝ . solution for every pair x, y of initial values from y A C X . The main result is a characterization of the generator of a C-cosine func
For a bounded linear injection C on a Banach space X and a closed linear ลฝ . ลฝ . operator A : D A ; X ยช X which commutes with C we prove that 1 the ลฝ . ลฝ . ลฝ . ลฝ . abstract Cauchy problem, uะ t s Au t , t g R, u 0 s Cx, uะ 0 s Cy, has a ลฝ . ลฝ . ลฝ 2 . unique strong solution for every x, y g D A if an