000 03670nam a22005295i 4500
001 978-3-642-12413-6
003 DE-He213
005 20140220084534.0
007 cr nn 008mamaa
008 100528s2010 gw | s |||| 0|eng d
020 _a9783642124136
_9978-3-642-12413-6
024 7 _a10.1007/978-3-642-12413-6
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
082 0 4 _a515.353
_223
100 1 _aKhapalov, Alexander Y.
_eauthor.
245 1 0 _aControllability of Partial Differential Equations Governed by Multiplicative Controls
_h[electronic resource] /
_cby Alexander Y. Khapalov.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2010.
300 _aXV, 284p. 26 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1995
505 0 _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.
520 _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.
650 0 _aMathematics.
650 0 _aDifferential equations, partial.
650 0 _aBiology
_xMathematics.
650 0 _aSystems theory.
650 0 _aHydraulic engineering.
650 1 4 _aMathematics.
650 2 4 _aPartial Differential Equations.
650 2 4 _aSystems Theory, Control.
650 2 4 _aCalculus of Variations and Optimal Control, Optimization.
650 2 4 _aMathematical Biology in General.
650 2 4 _aEngineering Fluid Dynamics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642124129
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1995
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-12413-6
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c112069
_d112069