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The abstract Cauchy problem

โœ Scribed by J.A Donaldson

Publisher
Elsevier Science
Year
1977
Tongue
English
Weight
474 KB
Volume
25
Category
Article
ISSN
0022-0396

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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

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C-Cosine Functions and the Abstract Cauchy Problem, II
โœ Chung-Cheng Kuo; Sen-Yen Shaw ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 246 KB

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, uะˆ 0 s Cy, has a ลฝ . ลฝ . ลฝ 2 . unique strong solution for every x, y g D A if an