LEADER 04668nam 22008415 450 001 996466494803316 005 20200701145509.0 010 $a1-280-39175-8 010 $a9786613569677 010 $a3-642-12471-2 024 7 $a10.1007/978-3-642-12471-6 035 $a(CKB)2550000000011509 035 $a(SSID)ssj0000449954 035 $a(PQKBManifestationID)11924072 035 $a(PQKBTitleCode)TC0000449954 035 $a(PQKBWorkID)10433429 035 $a(PQKB)10667260 035 $a(DE-He213)978-3-642-12471-6 035 $a(MiAaPQ)EBC3065342 035 $a(PPN)149063075 035 $a(EXLCZ)992550000000011509 100 $a20100601d2010 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aMutational Analysis$b[electronic resource] $eA Joint Framework for Cauchy Problems in and Beyond Vector Spaces /$fby Thomas Lorenz 205 $a1st ed. 2010. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2010. 215 $a1 online resource (XIV, 509 p. 57 illus. in color.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1996 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-642-12470-4 320 $aIncludes bibliographical references (p. 497-503) and indexes. 327 $aExtending Ordinary Differential Equations to Metric Spaces: Aubin?s Suggestion -- Adapting Mutational Equations to Examples in Vector Spaces: Local Parameters of Continuity -- Less Restrictive Conditions on Distance Functions: Continuity Instead of Triangle Inequality -- Introducing Distribution-Like Solutions to Mutational Equations -- Mutational Inclusions in Metric Spaces. 330 $aOrdinary differential equations play a central role in science and have been extended to evolution equations in Banach spaces. For many applications, however, it is difficult to specify a suitable normed vector space. Shapes without a priori restrictions, for example, do not have an obvious linear structure. This book generalizes ordinary differential equations beyond the borders of vector spaces with a focus on the well-posed Cauchy problem in finite time intervals. Here are some of the examples: - Feedback evolutions of compact subsets of the Euclidean space - Birth-and-growth processes of random sets (not necessarily convex) - Semilinear evolution equations - Nonlocal parabolic differential equations - Nonlinear transport equations for Radon measures - A structured population model - Stochastic differential equations with nonlocal sample dependence and how they can be coupled in systems immediately - due to the joint framework of Mutational Analysis. Finally, the book offers new tools for modelling. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1996 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aFunctions of real variables 606 $aDynamics 606 $aErgodic theory 606 $aDifferential equations 606 $aPartial differential equations 606 $aSystem theory 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 606 $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 0$aFunctions of real variables. 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aDifferential equations. 615 0$aPartial differential equations. 615 0$aSystem theory. 615 14$aAnalysis. 615 24$aReal Functions. 615 24$aDynamical Systems and Ergodic Theory. 615 24$aOrdinary Differential Equations. 615 24$aPartial Differential Equations. 615 24$aSystems Theory, Control. 676 $a515.35 686 $a34A60$a34G10$a35K20$a49J53$a60H20$a93B03$2msc 700 $aLorenz$b Thomas$4aut$4http://id.loc.gov/vocabulary/relators/aut$0478942 906 $aBOOK 912 $a996466494803316 996 $aMutational analysis$9261784 997 $aUNISA