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Invariance of closed convex sets under semigroups of nonlinear operators in complex Hilbert spaces
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On generation of nonlinear operator semigroups and nonlinear evolution operators
Semigroup Forum, 2003The basic semigroup generation result in \textit{M. G. Crandall} and \textit{A. Pazy} [Isr. J. Math. 11, 57--94 (1972; Zbl 0249.34049)] is re-obtained via sequential arguments based on difference equations theory.
Chin-Yuan Lin
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Invariance of closed convex sets under semigroups of nonlinear operators in complex Hilbert spaces
SUT Journal of Mathematics, 2001Let \(K\) be a closed convex subset of a complex Hilbert space \(H\) and \(A\) a nonlinear quasi-\(m\)-accretive operator with domain \(D(A)\) dense in \(H\) (that is, \(A+\alpha\) is \(m\)-accretive in \(H\) for some \(\alpha\geq 0)\). Then \(-A\) generates a nonlinear \(C_0\)-semigroup \(\{S(t)\}_{t\geq 0}\) of type \(\alpha\) on \(H\).
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Nonlinear Semigroups and Monotone Operators
Problem Books in Mathematics, 2011J W Neuberger, Neuberger J W
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Degenerate Nonlinear Semigroups of Operators and Their Applications
2020In this paper, we construct the conditions for the existence of a degenerate nonlinear resolving semigroup of shift operators for a semilinear Sobolev type equation. Based on the phase space method, we find the conditions for the existence of solutions to the Cauchy problem for a semilinear Sobolev type equation.
Ksenia V. Vasiuchkova +2 more
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