Results 131 to 140 of about 166,020,493 (162)

Invariance of closed convex sets under semigroups of nonlinear operators in complex Hilbert spaces

SUT Journal of Mathematics, 2001
Let \(K\) 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 \(H\).
exaly   +3 more sources

Degenerate Nonlinear Semigroups of Operators and Their Applications

2020
In 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, Natalia A. Manakova, Georgy A. Sviridyuk   +2 more
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On generation of C 0 semigroups and nonlinear operator semigroups

Semigroup Forum, 2002
This article presents new proofs (based on the theory of difference equations) of two classical theorems in the theory of semigroups of linear and nonlinear operators in a Banach space \(X\): the Hille-Phillips-Yosida theorem about generators of \(C_0\)-semigroups of bounded operators and the Crandall-Ligget theorem about generators of semigroups of ...
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AMENABLE SEMIGROUPS OF NONLINEAR OPERATORS IN UNIFORMLY CONVEX BANACH SPACES

Bulletin of the Australian Mathematical Society, 2018
In 1965, Browder proved the existence of a common fixed point for commuting families of nonexpansive mappings acting on nonempty bounded closed convex subsets of uniformly convex Banach spaces. The purpose of this paper is to extend this result to left amenable semigroups of nonexpansive mappings.
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Analytic semigroups, degenerate elliptic operators and applications to nonlinear cauchy problems

Annali di Matematica Pura ed Applicata, 1989
The nonlinear problem \[ u_ t=\phi (\Theta (u))\Delta (\chi (u)),\quad x\text{ in } {\bar \Omega},\quad t\geq 0;\quad u(x,0)=u_ 0(x) \] is considered, where \(\Omega\) is a bounded domain in \({\mathbb{R}}^ n\) with \({\mathbb{C}}^{\infty}\) boundary. \(\phi\), \(\Theta\), \(\chi\) are smooth functions and \(u_ 0\) is positive and sufficiently regular.
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Nonlinear Semigroups and Evolution Governed by Accretive Operators.

1984
Abstract : This is a review paper which outlines the main points of the theory of nonlinear semigroups and evolution governed by accretive operators. The subject is now rather mature, so most of the principal ideas and results are not new. However, the presentation here is organized differently from that in other sources and does touch upon recent ...
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Convergence of a hybrid algorithm for a reversible semigroup of nonlinear operators in Banach spaces

Nonlinear Analysis: Theory, Methods & Applications, 2010
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Inertial Invariant Manifolds of a Nonlinear Semigroup of Operators in a Hilbert Space

Journal of Mathematical Sciences
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On conditions of weak convergence of nonlinear contraction semigroups and of iterative methods for accretive operators in Banach spaces

Nonlinear Analysis: Theory, Methods & Applications, 1996
This paper relates to results of the authors about necessary and sufficient conditions are established for the strong convergence of the semigroup generated by an \(m\)-accretive operator \(A\) and of the steepest descent approximation process \[ x_{n+1}= x_n-t_nAx_n,\quad t_n\in\mathbb{R}^+,\quad \{t_n\}\not\in\ell^1 \] to a zero of a quasi-accretive ...
Jiang, Yao-Lin, Xu, Zong-Ben, Roach, G. F.   +2 more
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Maximal Accretive Operators, Nonlinear Nonexpansive Semigroups, and First-Order Evolution Equations

1990
In Chapter 30 we considered first-order evolution equations of the form (1) , with the operators A(t): V → V* and b(t) ∈ V* for all t ∈ ]0,T[. In this connection, “V ⊆ H ⊆ V*” is an evolution triple.
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