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008 | 040129s2002 pau b 001 0 eng d | ||
010 | _a 2001042994 | ||
011 | _aBIB MATCHES WORLDCAT | ||
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_a0898714869 _qpbk. |
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_a9780898714869 _qpbk. |
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035 | _a(ATU)b10818297 | ||
035 | _a(DLC) 2001042994 | ||
035 | _a(OCoLC)47254274 | ||
040 |
_aDLC _beng _erda _dATU |
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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 |
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245 | 1 | 0 |
_aMathematical control theory of coupled PDEs / _cIrena Lasiecka. |
264 | 1 |
_aPhiladelphia : _bSociety for Industrial and Applied Mathematics, _c[2002] |
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264 | 4 | _c©2002 | |
300 |
_axii, 242 pages ; _c25 cm. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_aunmediated _bn _2rdamedia |
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338 |
_avolume _bnc _2rdacarrier |
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490 | 1 |
_aCBMS-NSF regional conference series in applied mathematics ; _v75 |
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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 |
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_aDifferential equations, Hyperbolic _9337619 |
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_aDifferential equations, Parabolic _9330417 |
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650 | 0 |
_aCoupled mode theory _9329420 |
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830 | 0 |
_aCBMS-NSF regional conference series in applied mathematics ; _v75. _91046760 |
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907 |
_a.b10818297 _b11-07-17 _c27-10-15 |
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