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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On semigroups generated by $ m$-accretive operators in a strict sense

Author: Michiaki Watanabe
Journal: Proc. Amer. Math. Soc. 96 (1986), 43-49
MSC: Primary 47H20; Secondary 47H06
MathSciNet review: 813807
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Abstract: Let $ \left\{ {S(t):t \geqslant 0} \right\}$ be a nonlinear semigroup generated by an $ m$-accretive operator $ A$ in a real Banach space $ \left( {X,\left\vert \cdot \right\vert} \right)$. It is shown that (1) for any $ x \in D(A)$ belongs to $ {L^p}(0,T;V)(T < 0)$ if $ A$ satisfies

$\displaystyle {\left\vert {{u_1} - u} \right\vert^p} + C\lambda {\left\Vert {{u... ...nt {\left\vert {{u_1} + \lambda A{u_1} - {u_2} - \lambda A{u_2}} \right\vert^p}$

$ (p{\text{ > 1,}}C{\text{ > }}0)$ for $ \lambda {\text{ > }}0$ and $ {u_i} \in D(A)(i = 1,2)$, where $ \left( {V,\left\Vert \cdot \right\Vert} \right)$ is a Banach space including $ D(A)$ and included continuously in $ X$; and that (2) $ A + B$ has similar properties to those of the above $ A$ if $ B$ is a Lipschitz continuous operator from $ V$ to $ X$.

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Keywords: Semigroup, $ m$-accretive operator, perturbation
Article copyright: © Copyright 1986 American Mathematical Society

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