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Proceedings of the American Mathematical Society

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Existence of solutions to $ u'(t)=Au(t)$ for $ A$ weakly closed


Author: Shigeo Kanda
Journal: Proc. Amer. Math. Soc. 116 (1992), 121-126
MSC: Primary 47H20; Secondary 34G20
DOI: https://doi.org/10.1090/S0002-9939-1992-1102857-3
MathSciNet review: 1102857
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Abstract: We give an existence theorem of solutions to the evolution equation $ (d/dt)u(t) = Au(t)$ for a weakly closed operator $ A$ with some conditions on its resolvent in a reflexive Banach space.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1102857-3
Keywords: Evolution equation, weakly closed operator, Cauchy problem, reflexive Banach space
Article copyright: © Copyright 1992 American Mathematical Society