Convergence of Sequences of Semigroups of Nonlinear Operators With an Application to Gas Kinetics [PDF]
Transactions of the American Mathematical Society, 1973 Thomas G. Kurtz
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A Trotter-Lie Formula for Compactly Generated Semigroups of Nonlinear Operators
Journal of Functional Analysis, 1976 AbstractA Trotter-Lie type formula for semigroups of nonlinear operators on a Banach space X into itself, which are generated by compact operators, is proved.
A Pazy
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An Exponential Limit Formula for Nonlinear Semigroups
Transactions of the American Mathematical Society, 1970 In recent papers, many writers have developed the theory of semigroups of operators generated by nonlinear accretive operators. In the present paper, we construct this semigroup by means of an exponential limit formula, and then use this means of ...
Joel L. Mermin
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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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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 \(H\).
Tomomi Yokota
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A Proof-Theoretic Metatheorem for Nonlinear Semigroups Generated by an Accretive Operator and Applications [PDF]
Selecta Mathematica, New SeriesAbstract We further develop the theoretical framework of proof mining, a program in mathematical logic that seeks to quantify and extract computational information from prima facie ‘non-computational’ proofs from the mainstream mathematical literature.
Nicholas Norbert Pischke
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AMENABLE SEMIGROUPS OF NONLINEAR OPERATORS IN UNIFORMLY CONVEX BANACH SPACES
Bulletin of the Australian Mathematical Society, 2018In 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, 1989The 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.
1984Abstract : 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, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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