Existence of solutions to an evolution equation and a justification of the DSM for equations with monotone operators

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dc.contributor.author Ramm, Alexander G.
dc.contributor.author Hoang, N. S.
dc.date.accessioned 2011-06-15T20:00:55Z
dc.date.available 2011-06-15T20:00:55Z
dc.date.issued 2011-06-15
dc.identifier.uri http://hdl.handle.net/2097/9250
dc.description.abstract An evolution equation, arising in the study of the Dynamical Systems Method (DSM)for solving equations with monotone operators, is studied in this paper. The evolution equation is a continuous analog of the regularized Newton method for solving ill-posed problems with monotone nonlinear operators F. Local and global existence of the unique solution to this evolution equation are proved, apparently for the first time, under only the assumption that F′(u) exists and is continuous with respect to u. The earlier published results required more smoothness of F. The Dynamical Systems Method (DSM) for solving equations F(u)=0 with monotone Fr´echet differentiable operator F is justified under the above assumption apparently for the first time. en_US
dc.relation.uri http://www.intlpress.com/CMS/ en_US
dc.rights This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). en_US
dc.rights.uri http://rightsstatements.org/vocab/InC/1.0/
dc.subject Dynamical Systems Method (DSM) en_US
dc.subject Nonlinear operator equations en_US
dc.subject Monotone operators en_US
dc.title Existence of solutions to an evolution equation and a justification of the DSM for equations with monotone operators en_US
dc.type Article (publisher version) en_US
dc.date.published 2009 en_US
dc.citation.epage 1079 en_US
dc.citation.issue 4 en_US
dc.citation.jtitle Communications in Mathematical Sciences en_US
dc.citation.spage 1073 en_US
dc.citation.volume 7 en_US
dc.contributor.authoreid ramm en_US
dc.contributor.authoreid nguyenhs en_US


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