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Symmetrization and stabilization of solutions of nonlinear elliptic equations

This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for...

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Detalles Bibliográficos
Autor principal: Efendiev, Messoud
Lenguaje:eng
Publicado: Springer 2018
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-98407-0
http://cds.cern.ch/record/2647177
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author Efendiev, Messoud
author_facet Efendiev, Messoud
author_sort Efendiev, Messoud
collection CERN
description This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as finite dimensional reduction of their dynamics requires new ideas and tools. To this end, both a trajectory dynamical systems approach and new Liouville type results for the solutions of some class of elliptic equations are used. The work also uses symmetry and monotonicity results for nonnegative solutions in order to characterize an asymptotic profile of solutions and compares a pure elliptic partial differential equations approach and a dynamical systems approach. The new results obtained will be particularly useful for mathematical biologists.
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institution Organización Europea para la Investigación Nuclear
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spelling cern-26471772021-04-21T18:40:37Zdoi:10.1007/978-3-319-98407-0http://cds.cern.ch/record/2647177engEfendiev, MessoudSymmetrization and stabilization of solutions of nonlinear elliptic equationsMathematical Physics and MathematicsThis book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as finite dimensional reduction of their dynamics requires new ideas and tools. To this end, both a trajectory dynamical systems approach and new Liouville type results for the solutions of some class of elliptic equations are used. The work also uses symmetry and monotonicity results for nonnegative solutions in order to characterize an asymptotic profile of solutions and compares a pure elliptic partial differential equations approach and a dynamical systems approach. The new results obtained will be particularly useful for mathematical biologists.Springeroai:cds.cern.ch:26471772018
spellingShingle Mathematical Physics and Mathematics
Efendiev, Messoud
Symmetrization and stabilization of solutions of nonlinear elliptic equations
title Symmetrization and stabilization of solutions of nonlinear elliptic equations
title_full Symmetrization and stabilization of solutions of nonlinear elliptic equations
title_fullStr Symmetrization and stabilization of solutions of nonlinear elliptic equations
title_full_unstemmed Symmetrization and stabilization of solutions of nonlinear elliptic equations
title_short Symmetrization and stabilization of solutions of nonlinear elliptic equations
title_sort symmetrization and stabilization of solutions of nonlinear elliptic equations
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-98407-0
http://cds.cern.ch/record/2647177
work_keys_str_mv AT efendievmessoud symmetrizationandstabilizationofsolutionsofnonlinearellipticequations