On an abstract evolution equation with a spectral operator of scalar type
It is shown that the weak solutions of the evolution equation y′(t)=Ay(t), t∈[0,T) (0<T≤∞), where A is a spectral operator of scalar type in a complex Banach space X, defined by Ball (1977), are given by the formula y(t)=e tAf, t∈[0,T), with the exponentials understood in the sense of the operati...
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202112233 |
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| Summary: | It is shown that the weak solutions of the evolution equation y′(t)=Ay(t), t∈[0,T) (0<T≤∞), where A is a spectral operator of scalar type in a complex Banach space X, defined by Ball (1977), are given by the formula y(t)=e tAf, t∈[0,T), with the exponentials understood in the sense of the operational calculus for such operators and the set of the initial values, f's, being ∩ 0≤t<TD(e tA), that is, the largest possible such a set in X. |
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| ISSN: | 0161-1712 1687-0425 |