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100   $a20181017d2018      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aSymmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations /$fby Messoud Efendiev
205   $a1st ed. 2018.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018.
215   $a1 online resource (273 pages)
225 1 $aFields Institute Monographs,$x1069-5273 ;$v36
311   $a3-319-98406-3 
327   $aPreface -- 1. Preliminaries -- 2. Trajectory dynamical systems and their attractors -- 3. Symmetry and attractors: the case N ? 3 -- 4. Symmetry and attractors: the case N ? 4 -- 5. Symmetry and attractors -- 6. Symmetry and attractors: arbitrary dimension -- 7. The case of p-Laplacian operator -- Bibliography. .
330   $aThis book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as finite dimensional reduction of their dynamics requires new ideas and tools. To this end, both a trajectory dynamical systems approach and new Liouville type results for the solutions of some class of elliptic equations are used. The work also uses symmetry and monotonicity results for nonnegative solutions in order to characterize an asymptotic profile of solutions and compares a pure elliptic partial differential equations approach and a dynamical systems approach. The new results obtained will be particularly useful for mathematical biologists.
410  0$aFields Institute Monographs,$x1069-5273 ;$v36
606   $aPartial differential equations
606   $aDynamics
606   $aErgodic theory
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
606   $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X
615  0$aPartial differential equations.
615  0$aDynamics.
615  0$aErgodic theory.
615 14$aPartial Differential Equations.
615 24$aDynamical Systems and Ergodic Theory.
676   $a515.353
700   $aEfendiev$b Messoud$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767841
906   $aBOOK
912   $a9910300135303321
996   $aSymmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations$91563791
997   $aUNINA