Regularity of solutions to an abstract inhomogeneous linear differential equation
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- by G. F. Webb PDF
- Proc. Amer. Math. Soc. 62 (1977), 271-277 Request permission
Abstract:
Let $T(t),t \geqslant 0$, be a strongly continuous semigroup of linear operators on a Banach space X with infinitesimal generator A satisfying $T(t)X \subset D(A)$ for all $t > 0$. Let f be a function from $[0,\infty )$ to X of strong bounded variation. It is proved that $u(t){ = ^{{\text {def}}}}T(t)x + {\smallint ^{t0}}T(t - s)f(s)ds,x \in X$, is strongly differentiable and satisfies $du(t)/dt = Au(t) + f(t)$ for all but a countable number of $t > 0$.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 62 (1977), 271-277
- MSC: Primary 34G05; Secondary 47D05
- DOI: https://doi.org/10.1090/S0002-9939-1977-0432996-3
- MathSciNet review: 0432996