Geodesic
On computational properties of Cauchy problems generated by accretive operators
Documenta mathematica, Tome 28 (2023) no. 5, pp. 1235-1274

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In this paper, we provide quantitative versions of results on the asymptotic behavior of nonlinear semigroups generated by an accretive operator due to O. Nevanlinna and S. Reich as well as H.-K. Xu. These results themselves rely on a particular assumption on the underlying operator introduced by A. Pazy under the name of “convergence condition”. Based on logical techniques from “proof mining”, a subdiscipline of mathematical logic, we derive various notions of a “convergence condition with modulus” which provide quantitative information on this condition in different ways. These techniques then also facilitate the extraction of quantitative information on the convergence results of Nevanlinna and Reich as well as Xu, in particular also in the form of rates of convergence which depend on these moduli for the convergence condition.
DOI : 10.4171/dm/924
Classification : 47H20, 47H06, 35F25, 03F10
Mots-clés : Accretive operators, nonlinear semigroups, partial differential equations, rates of convergence, proof mining 
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Pedro Pinto; Nicholas Pischke. On computational properties of Cauchy problems generated by accretive operators. Documenta mathematica, Tome 28 (2023) no. 5, pp. 1235-1274. doi: 10.4171/dm/924

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