LEADER 04812nam 22007335 450 001 996466494403316 005 20200701195734.0 010 $a1-280-39173-1 010 $a9786613569653 010 $a3-642-12413-5 024 7 $a10.1007/978-3-642-12413-6 035 $a(CKB)2550000000011508 035 $a(SSID)ssj0000449264 035 $a(PQKBManifestationID)11303967 035 $a(PQKBTitleCode)TC0000449264 035 $a(PQKBWorkID)10429115 035 $a(PQKB)10352803 035 $a(DE-He213)978-3-642-12413-6 035 $a(MiAaPQ)EBC3065286 035 $a(PPN)149078587 035 $a(EXLCZ)992550000000011508 100 $a20100528d2010 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aControllability of Partial Differential Equations Governed by Multiplicative Controls$b[electronic resource] /$fby Alexander Y. Khapalov 205 $a1st ed. 2010. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2010. 215 $a1 online resource (XV, 284 p. 26 illus.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1995 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-642-12412-7 320 $aIncludes bibliographical references (p. 275-281) and index. 327 $aMultiplicative Controllability of Parabolic Equations -- Global Nonnegative Controllability of the 1-D Semilinear Parabolic Equation -- Multiplicative Controllability of the Semilinear Parabolic Equation: A Qualitative Approach -- The Case of the Reaction-Diffusion Term Satisfying Newton?s Law -- Classical Controllability for the Semilinear Parabolic Equations with Superlinear Terms -- Multiplicative Controllability of Hyperbolic Equations -- Controllability Properties of a Vibrating String with Variable Axial Load and Damping Gain -- Controllability Properties of a Vibrating String with Variable Axial Load Only -- Reachability of Nonnegative Equilibrium States for the Semilinear Vibrating String -- The 1-D Wave and Rod Equations Governed by Controls That Are Time-Dependent Only -- Controllability for Swimming Phenomenon -- A ?Basic? 2-D Swimming Model -- The Well-Posedness of a 2-D Swimming Model -- Geometric Aspects of Controllability for a Swimming Phenomenon -- Local Controllability for a Swimming Model -- Global Controllability for a ?Rowing? Swimming Model -- Multiplicative Controllability Properties of the Schrodinger Equation -- Multiplicative Controllability for the Schrödinger Equation. 330 $aThe goal of this monograph is to address the issue of the global controllability of partial differential equations in the context of multiplicative (or bilinear) controls, which enter the model equations as coefficients. The mathematical models we examine include the linear and nonlinear parabolic and hyperbolic PDE's, the Schrödinger equation, and coupled hybrid nonlinear distributed parameter systems modeling the swimming phenomenon. The book offers a new, high-quality and intrinsically nonlinear methodology to approach the aforementioned highly nonlinear controllability problems. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1995 606 $aPartial differential equations 606 $aSystem theory 606 $aCalculus of variations 606 $aBiomathematics 606 $aFluid mechanics 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 606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016 606 $aMathematical and Computational Biology$3https://scigraph.springernature.com/ontologies/product-market-codes/M31000 606 $aEngineering Fluid Dynamics$3https://scigraph.springernature.com/ontologies/product-market-codes/T15044 615 0$aPartial differential equations. 615 0$aSystem theory. 615 0$aCalculus of variations. 615 0$aBiomathematics. 615 0$aFluid mechanics. 615 14$aPartial Differential Equations. 615 24$aSystems Theory, Control. 615 24$aCalculus of Variations and Optimal Control; Optimization. 615 24$aMathematical and Computational Biology. 615 24$aEngineering Fluid Dynamics. 676 $a515.353 700 $aKhapalov$b Alexander Y$4aut$4http://id.loc.gov/vocabulary/relators/aut$0478941 906 $aBOOK 912 $a996466494403316 996 $aControllability of partial differential equations governed by multiplicative controls$9261787 997 $aUNISA