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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Regularizing properties of nonlinear semigroups
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by Semion Gutman PDF
Proc. Amer. Math. Soc. 101 (1987), 51-56 Request permission

Abstract:

It is known that some classes of $m$-accretive operators $A$ generate Lipschitz continuous semigroups of contractions; that is $||S(t + h)x - S(t)x|| \leqslant L(||x||)h/t,0 \leqslant t \leqslant t + h \leqslant T,x \in \overline {D(A)}$. If the underlying Banach spaces $X$ and ${X^*}$ are uniformly convex and an $m$-accretive operator $B$ is bounded, we prove, in particular, that the semigroup generated by $A + B$ is Hölder continuous. The proof is based on a result on the structure of accretive operators obtained via the Kuratowski-Ryll-Nardzewski Selection Theorem. Also, we consider some applications of these results to the existence of solutions of $u’ + Au + Bu \backepsilon Cu,u(0) = {u_0}$.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 101 (1987), 51-56
  • MSC: Primary 47H20; Secondary 34G20, 35R20, 47H06
  • DOI: https://doi.org/10.1090/S0002-9939-1987-0897069-0
  • MathSciNet review: 897069