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010 _a 2001042994
011 _aBIB MATCHES WORLDCAT
020 _a0898714869
_qpbk.
020 _a9780898714869
_qpbk.
035 _a(ATU)b10818297
035 _a(DLC) 2001042994
035 _a(OCoLC)47254274
040 _aDLC
_beng
_erda
_dATU
042 _apcc
050 0 0 _aQA402.3
_b.L333 2002
082 0 0 _a629.8312
_221
100 1 _aLasiecka, I.
_q(Irena),
_d1948-
_eauthor.
_9257785
245 1 0 _aMathematical control theory of coupled PDEs /
_cIrena Lasiecka.
264 1 _aPhiladelphia :
_bSociety for Industrial and Applied Mathematics,
_c[2002]
264 4 _c©2002
300 _axii, 242 pages ;
_c25 cm.
336 _atext
_btxt
_2rdacontent
337 _aunmediated
_bn
_2rdamedia
338 _avolume
_bnc
_2rdacarrier
490 1 _aCBMS-NSF regional conference series in applied mathematics ;
_v75
504 _aIncludes bibliographical references (pages 225-238) and index.
505 0 0 _tPreface --
_g1.
_tIntroduction --
_g1.1.
_tControl Theory of Dynamical PDEs --
_g1.1.1.
_tFinite- versus infinite-dimensional control theory --
_g1.1.2.
_tBoundary/point control problems for single PDEs --
_g1.1.3.
_tBoundary/point control problems for systems of coupled PDEs --
_g1.2.
_tGoal of the Lectures --
_g2.
_tWell-Posedness of Second-Order Nonlinear Equations with Boundary Damping --
_g2.1.
_tOrientation --
_g2.2.
_tAbstract Model --
_g2.3.
_tExistence and Uniqueness: Statement of Main Results --
_g2.4.
_tNonlinear Plates: von Karman Equations --
_g2.4.1.
_tCase [gamma] > 0 --
_g2.4.2.
_tCase [gamma] = 0 --
_g2.5.
_tSemilinear Wave Equation --
_g2.6.
_tNonlinear Structural Acoustic Model --
_g2.7.
_tFull von Karman Systems --
_g2.7.1.
_tModel --
_g2.7.2.
_tFormulation of the results: Case [gamma] = 0 --
_g2.7.3.
_tFormulation of the results: Case [gamma] > 0 --
_g2.8.
_tComments and Open Problems --
_g3.
_tUniform Stabilizability of Nonlinear Waves and Plates --
_g3.1.
_tOrientation --
_g3.2.
_tAbstract Stabilization Inequalities --
_g3.3.
_tSemilinear Wave Equation with Nonlinear Boundary Damping --
_g3.3.1.
_tFormulation of the results --
_g3.3.2.
_tRegularization --
_g3.3.3.
_tPreliminary PDE inequalities --
_g3.3.4.
_tAbsorption of the lower-order terms --
_g3.3.5.
_tCompletion of the proof of the main theorem --
_g3.4.
_tNonlinear Plate Equations --
_g3.4.1.
_tModified von Karman equations --
_g3.4.2.
_tFull von Karman system and dynamic system of elasticity --
_g3.4.3.
_tNonlinear plates with thermoelasticity --
_g3.5.
_tComments and Open Problems --
_g4.
_tUniform Stability of Structural Acoustic Models --
_g4.1.
_tOrientation --
_g4.2.
_tInternal Damping on the Wall --
_g4.3.
_tBoundary Damping on the Wall --
_g4.3.1.
_tModel --
_g4.3.2.
_tFormulation of the results --
_g4.3.3.
_tPreliminary multipliers estimates --
_g4.3.4.
_tMicroanalysis estimate for the traces of solutions of Euler-Bernoulli equations and wave equations --
_g4.3.5.
_tObservability estimates for the structural acoustic problem --
_g4.3.6.
_tCompletion of the proof of Theorem 4.3.1 --
_g4.4.
_tThermal Damping --
_g4.4.1.
_tModel --
_g4.4.2.
_tStatement of main results --
_g4.4.3.
_tSharp trace regularity results --
_g4.4.4.
_tUniform stabilization: Proof of Theorem 4.4.2 --
_g4.4.5.
_tWave equation --
_g4.4.6.
_tUniform stability analysis for the coupled system --
_g4.5.
_tComments and Open Problems --
_g5.
_tStructural Acoustic Control Problems: Semigroup and PDE Models --
_g5.1.
_tOrientation --
_g5.2.
_tAbstract Setting: Semigroup Formulation --
_g5.3.
_tPDE Models Illustrating the Abstract Wall Equation (5.2.2) --
_g5.3.1.
_tPlates and beams: Flat[Gamma subscript 0] --
_g5.3.2.
_t"Undamped" boundary conditions: g [identical with] 0 in (5.3.10) --
_g5.3.3.
_tBoundary feedback: Case g [not equal] 0 in (5.3.10) and related stability --
_g5.3.4.
_tShells: Curved-wall [Gamma subscript 0] --
_g5.4.
_tStability in Linear Structural Acoustic Models --
_g5.4.1.
_tInternal damping on the wall --
_g5.4.2.
_tBoundary damping on the wall --
_g5.5.
_tComments and Open Problems --
_g6.
_tFeedback Noise Control in Structural Acoustic Models: Finite Horizon Problems --
_g6.1.
_tOrientation --
_g6.2.
_tOptimal Control Problem --
_g6.3.
_tFormulation of the Results --
_g6.3.1.
_tHyperbolic-parabolic coupling --
_g6.3.2.
_tHyperbolic-hyperbolic coupling: General case --
_g6.3.3.
_tHyperbolic-hyperbolic coupling: Special case of the Kirchhoff plate with point control --
_g6.4.
_tAbstract Optimal Control Problem: General Theory --
_g6.4.1.
_tFormulation of the abstract control problem --
_g6.4.2.
_tCharacterization of the optimal control --
_g6.4.3.
_tAdditional properties under the hyperbolic regularity assumption --
_g6.4.4.
_tDRE, feedback generator, and regularity of the gains B*P, B*r --
_g6.5.
_tRiccati Equations Subject to the Singular Estimate for e[superscript At]B --
_g6.5.1.
_tFormulation of the results --
_g6.5.2.
_tProof of Lemma 6.5.1 --
_g6.5.3.
_tProof of Theorem 6.5.1 --
_g6.6.
_tBack to Structural Acoustic Problems: Proofs of Theorems 6.3.1 and 6.3.2 --
_g6.6.1.
_tVerification of Assumption (6.4.1) --
_g6.6.2.
_tVerification of Assumption 6.5.1 --
_g6.7.
_tComments and Open Problems --
_g7.
_tFeedback Noise Control in Structural Acoustic Models: Infinite Horizon Problems --
_g7.1.
_tOrientation --
_g7.2.
_tOptimal Control Problem --
_g7.3.
_tFormulation of the Results --
_g7.3.1.
_tHyperbolic-parabolic coupling --
_g7.3.2.
_tHyperbolic-hyperbolic coupling: Abstract results --
_g7.3.3.
_tHyperbolic-hyperbolic coupling: Kirchhoff plate with point control --
_g7.4.
_tAbstract Optimal Control Problem: General Theory --
_g7.4.1.
_tFormulation of the abstract control problem --
_g7.4.2.
_tARE subject to condition (7.4.15) --
_g7.5.
_tARE Subject to a Singular Estimate for e[superscript At]B --
_g7.5.1.
_tFormulation of the results --
_g7.5.2.
_tProof of Theorem 7.5.1 --
_g7.6.
_tBack to Structural Acoustic Problems: Proofs of Theorems 7.3.1 and 7.3.2 --
_g7.7.
_tComments and Open Problems --
_tBibliography --
_tIndex.
588 _aMachine converted from AACR2 source record.
650 0 _aControl theory
_9316031
650 0 _aDifferential equations, Hyperbolic
_9337619
650 0 _aDifferential equations, Parabolic
_9330417
650 0 _aCoupled mode theory
_9329420
830 0 _aCBMS-NSF regional conference series in applied mathematics ;
_v75.
_91046760
907 _a.b10818297
_b11-07-17
_c27-10-15
942 _cB
945 _a629.8312 LAS
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