differential equations and control theory differential equations and control theory edited by Sergiu Aizicovici Nicolae H. Pavel Ohio University Athens, Ohio MARCEL DEKKER, INC. NEW YORK • BASEL ISBN: 0-8247-0681-1 This book is printed on acid-free paper. Headquarters Marcel Dekker, Inc. 270 Madison Avenue, New York, NY 10016 tel: 212-696-9000; fax: 212-685-4540 Eastern Hemisphere Distribution Marcel Dekker AG Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland tel: 41-61-261-8482; fax: 41-61-261-8896 World Wide Web http://www.dekker.com The publisher offers discounts on this book when ordered in bulk quantities. For more information, write to Special Sales/Professional Marketing at the headquarters address above. Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved. 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Current printing (last digit): 10 9 8 7 6 5 4 3 21 PRINTED IN THE UNITED STATES OF AMERICA PUREANDAPPLIEDMATHEMATICS AProgramofMonographs,Textbooks,andLectureNotes EXECUTIVEEDITORS EarlJ.Taft ZuhairNashed RutgersUniversity UniversityofCentralFlorida NewBrunswick,NewJersey Orlando,Florida EDITORIALBOARD M.S.Baouendi AnilNerode UniversityofCalifornia, CornellUniversity SanDiego DonaldPassman JaneCronin UniversityofWisconsin, RutgersUniversity Madison JackK.Hale FredS.Roberts GeorgiaInstituteofTechnology RutgersUniversity S.Kobayashi DavidL.Russell UniversityofCalifornia, VirginiaPolytechnicInstitute Berkeley andStateUniversity MarvinMarcus WalterSchempp UniversityofCalifornia, UniversitätSiegen SantaBarbara MarkTeply W.S.Massey UniversityofWisconsin, YaleUniversity Milwaukee LECTURENOTESINPUREANDAPPLIEDMATHEMATICS 1. N.Jacobson,ExceptionalLieAlgebras 2. L.-Å.LindahlandF.Poulsen,ThinSetsinHarmonicAnalysis 3. I.Satake,ClassificationTheoryofSemi-SimpleAlgebraicGroups 4. F.Hirzebruchetal.,DifferentiableManifoldsandQuadraticForms 5. I.Chavel,RiemannianSymmetricSpacesofRankOne 6. R.B.Burckel,CharacterizationofC(X)AmongItsSubalgebras 7. B.R.McDonaldetal.,RingTheory 8. Y.-T.Siu,TechniquesofExtensiononAnalyticObjects 9. S.R.Caradusetal.,CalkinAlgebrasandAlgebrasofOperatorsonBanachSpaces 10. E.O.Roxinetal.,DifferentialGamesandControlTheory 11. M.OrzechandC.Small,TheBrauerGroupofCommutativeRings 12. S.Thomier,TopologyandItsApplications 13. J.M.LopezandK.A.Ross,SidonSets 14. W.W.ComfortandS.Negrepontis,ContinuousPseudometrics 15. K.McKennonandJ.M.Robertson,LocallyConvexSpaces 16. M.CarmeliandS.Malin,RepresentationsoftheRotationandLorentzGroups 17. G.B.Seligman,RationalMethodsinLieAlgebras 18. D.G.deFigueiredo,FunctionalAnalysis 19. L.Cesarietal.,NonlinearFunctionalAnalysisandDifferentialEquations 20. J.J.Schäffer,GeometryofSpheresinNormedSpaces 21. K.YanoandM.Kon,Anti-InvariantSubmanifolds 22. W.V.Vasconcelos,TheRingsofDimensionTwo 23. R.E.Chandler,HausdorffCompactifications 24. S.P.FranklinandB.V.S.Thomas,Topology 25. S.K.Jain,RingTheory 26. B.R.McDonaldandR.A.Morris,RingTheoryII 27. R.B.MuraandA.Rhemtulla,OrderableGroups 28. J.R.Graef,StabilityofDynamicalSystems 29. H.-C.Wang,HomogeneousBranchAlgebras 30. E.O.Roxinetal.,DifferentialGamesandControlTheoryII 31. R.D.Porter,IntroductiontoFibreBundles 32. M.Altman,ContractorsandContractorDirectionsTheoryandApplications 33. J.S.Golan,DecompositionandDimensioninModuleCategories 34. G.Fairweather,FiniteElementGalerkinMethodsforDifferentialEquations 35. J.D.Sally,NumbersofGeneratorsofIdealsinLocalRings 36. S.S.Miller,ComplexAnalysis 37. R.Gordon,RepresentationTheoryofAlgebras 38. M.GotoandF.D.Grosshans,SemisimpleLieAlgebras 39. A.I.Arrudaetal.,MathematicalLogic 40. F.VanOystaeyen,RingTheory 41. F.VanOystaeyenandA.Verschoren,ReflectorsandLocalization 42. M.Satyanarayana,PositivelyOrderedSemigroups 43. D.LRussell,MathematicsofFinite-DimensionalControlSystems 44. P.-T.LiuandE.Roxin,DifferentialGamesandControlTheoryIII 45. A.GeramitaandJ.Seberry,OrthogonalDesigns 46. J. Cigler, V. Losert, and P. Michor, Banach Modules and Functors on Categories of Banach Spaces 47. P.-T.LiuandJ.G.Sutinen,ControlTheoryinMathematicalEconomics 48. C.Byrnes,PartialDifferentialEquationsandGeometry 49. G.Klambauer,ProblemsandPropositionsinAnalysis 50. J.Knopfmacher,AnalyticArithmeticofAlgebraicFunctionFields 51. F.VanOystaeyen,RingTheory 52. B.Kadem,BinaryTimeSeries 53. J.Barros-NetoandR.A.Artino,HypoellipticBoundary-ValueProblems 54. R.L.Sternbergetal.,NonlinearPartialDifferentialEquationsinEngineeringandAppliedScience 55. B.R.McDonald,RingTheoryandAlgebraIII 56. J.S.Golan,StructureSheavesOveraNoncommutativeRing 57. T.V.Narayanaetal.,Combinatorics,RepresentationTheoryandStatisticalMethodsinGroups 58. T.A.Burton,ModelingandDifferentialEquationsinBiology 59. K.H.KimandF.W.Roush,IntroductiontoMathematicalConsensusTheory 60. J.BanasandK.Goebel,MeasuresofNoncompactnessinBanachSpaces 61. O.A.Nielson,DirectIntegralTheory 62. J.E.Smithetal.,OrderedGroups 63. J.Cronin,MathematicsofCellElectrophysiology 64. J.W.Brewer,PowerSeriesOverCommutativeRings 65. P.K.KamthanandM.Gupta, SequenceSpacesandSeries 66. T.G.McLaughlin,RegressiveSetsandtheTheoryofIsols 67. T.L.Herdmanetal.,IntegralandFunctionalDifferentialEquations 68. R.Draper,CommutativeAlgebra 69. W. G. McKay and J. Patera, Tables of Dimensions, Indices, and Branching Rules for Repre- sentationsofSimpleLieAlgebras 70. R.L.DevaneyandZ.H.Nitecki,ClassicalMechanicsandDynamicalSystems 71. J.VanGeel,PlacesandValuationsinNoncommutativeRingTheory 72. C.Faith,InjectiveModulesandInjectiveQuotientRings 73. A.Fiacco,MathematicalProgrammingwithDataPerturbationsI 74. P.Schultzetal.,AlgebraicStructuresandApplications 75. LBicanetal.,Rings,Modules,andPreradicals 76. D.C.KayandM.Breen,ConvexityandRelatedCombinatorialGeometry 77. P.FletcherandW.F.Lindgren,Quasi-UniformSpaces 78. C.-C.Yang,FactorizationTheoryofMeromorphicFunctions 79. O.Taussky,TernaryQuadraticFormsandNorms 80. S.P.SinghandJ.H.Burry,NonlinearAnalysisandApplications 81. K.B.Hannsgenetal.,VolterraandFunctionalDifferentialEquations 82. N.L.Johnsonetal.,FiniteGeometries 83. G.I.Zapata,FunctionalAnalysis,Holomorphy,andApproximationTheory 84. S.GrecoandG.Valla,CommutativeAlgebra 85. A.V.Fiacco,MathematicalProgrammingwithDataPerturbationsII 86. J.-B.Hiriart-Urrutyetal.,Optimization 87. A.FigaTalamancaandM.A.Picardello,HarmonicAnalysisonFreeGroups 88. M.Harada,FactorCategorieswithApplicationstoDirectDecompositionofModules 89. V.I.Istra'tescu,StrictConvexityandComplexStrictConvexity 90. V.Lakshmikantham,TrendsinTheoryandPracticeofNonlinearDifferentialEquations 91. H.L.ManochaandJ.B.Srivastava,AlgebraandItsApplications 92. D. V. Chudnovsky and G. V. Chudnovsky, Classical and Quantum Models and Arithmetic Problems 93. J.W.Longley,LeastSquaresComputationsUsingOrthogonalizationMethods 94. L.P.deAlcantara,MathematicalLogicandFormalSystems 95. C.E.Aull,RingsofContinuousFunctions 96. R.Chuaqui,Analysis,Geometry,andProbability 97. L.FuchsandL.Salce,ModulesOverValuationDomains 98. P.FischerandW.R.Smith,Chaos,Fractals,andDynamics 99. W.B.PowellandC.Tsinakis,OrderedAlgebraicStructures 100. G. M. Rassias and T. M. Rassias, Differential Geometry, Calculus of Variations, and Their Applications 101. R.-E.HoffmannandK.H.Hofmann,ContinuousLatticesandTheirApplications 102. J.H.LightbourneIIIandS.M.RankinIII,PhysicalMathematicsandNonlinearPartialDifferential Equations 103. C.A.BakerandL.M.Batten,FiniteGeometrics 104. J.W.Breweretal.,LinearSystemsOverCommutativeRings 105. C.McCroryandT.Shifrin,GeometryandTopology 106. D.W.Kuekeetal.,MathematicalLogicandTheoreticalComputerScience 107. B.-L.LinandS.Simons,NonlinearandConvexAnalysis 108. S.J.Lee,OperatorMethodsforOptimalControlProblems 109. V.Lakshmikantham,NonlinearAnalysisandApplications 110. S.F.McCormick,MultigridMethods 111. M.C.Tangora,ComputersinAlgebra 112. D.V.ChudnovskyandG.V.Chudnovsky,SearchTheory 113. D.V.ChudnovskyandR.D.Jenks,ComputerAlgebra 114. M.C.Tangora,ComputersinGeometryandTopology 115. P.Nelsonetal.,TransportTheory,InvariantImbedding,andIntegralEquations 116. P.Clémentetal.,SemigroupTheoryandApplications 117. J.Vinuesa,OrthogonalPolynomialsandTheirApplications 118. C.M.Dafermosetal.,DifferentialEquations 119. E.O.Roxin,ModernOptimalControl 120. J.C.Díaz,MathematicsforLargeScaleComputing 121. P.S.MilojevicÚ,NonlinearFunctionalAnalysis 122. C.Sadosky,AnalysisandPartialDifferentialEquations 123. R.M.Shortt,GeneralTopologyandApplications 124. R.Wong,AsymptoticandComputationalAnalysis 125. D.V.ChudnovskyandR.D.Jenks,ComputersinMathematics 126. W.D.Wallisetal.,CombinatorialDesignsandApplications 127. S.Elaydi,DifferentialEquations 128. G.Chenetal.,DistributedParameterControlSystems 129. W.N.Everitt,Inequalities 130. H. G. Kaper and M. Garbey, Asymptotic Analysis and the Numerical Solution of Partial Differ- entialEquations 131. O.Arinoetal.,MathematicalPopulationDynamics 132. S.Coen,GeometryandComplexVariables 133. J. A. Goldstein et al., Differential Equations with Applications in Biology, Physics, and Engineering 134. S.J.Andimaetal.,GeneralTopologyandApplications 135. PClémentetal.,SemigroupTheoryandEvolutionEquations 136. K.Jarosz,FunctionSpaces 137. J.M.Bayodetal.,p-adicFunctionalAnalysis 138. G.A.Anastassiou,ApproximationTheory 139. R.S.Rees,Graphs,Matrices,andDesigns 140. G.Abramsetal.,MethodsinModuleTheory 141. G.L.MullenandP.J.-S.Shiue,FiniteFields,CodingTheory,andAdvancesinCommunications andComputing 142. M.C.JoshiandA.V.Balakrishnan,MathematicalTheoryofControl 143. G.KomatsuandY.Sakane,ComplexGeometry 144. I.J.Bakelman,GeometricAnalysisandNonlinearPartialDifferentialEquations 145. T.MabuchiandS.Mukai,EinsteinMetricsandYang–MillsConnections 146. L.FuchsandR.Göbel,AbelianGroups 147. A.D.PollingtonandW.Moran,NumberTheorywithanEmphasisontheMarkoffSpectrum 148. G.Doreetal.,DifferentialEquationsinBanachSpaces 149. T.West,ContinuumTheoryandDynamicalSystems 150. K.D.Bierstedtetal.,FunctionalAnalysis 151. K.G.Fischeretal.,ComputationalAlgebra 152. K.D.Elworthyetal.,DifferentialEquations,DynamicalSystems,andControlScience 153. P.-J.Cahen,etal.,CommutativeRingTheory 154. S.C.CooperandW.J.Thron,ContinuedFractionsandOrthogonalFunctions 155. P.ClémentandG.Lumer,EvolutionEquations,ControlTheory,andBiomathematics 156. M.GyllenbergandL.Persson,Analysis,Algebra,andComputersinMathematicalResearch 157. W.O.Brayetal.,FourierAnalysis 158. J.BergenandS.Montgomery,AdvancesinHopfAlgebras 159. A.R.Magid,Rings,Extensions,andCohomology 160. N.H.Pavel,OptimalControlofDifferentialEquations 161. M.Ikawa,SpectralandScatteringTheory 162. X.LiuandD.Siegel,ComparisonMethodsandStabilityTheory 163. J.-P.Zolésio,BoundaryControlandVariation 164. M.Kr'íz''eketal.,FiniteElementMethods 165. G.DaPratoandL.Tubaro,ControlofPartialDifferentialEquations 166. E.Ballico,ProjectiveGeometrywithApplications 167. M.Costabeletal.,BoundaryValueProblemsandIntegralEquationsinNonsmoothDomains 168. G.Ferreyra,G.R.Goldstein,andF.Neubrander,EvolutionEquations 169. S.Huggett,TwistorTheory 170. H.Cooketal.,Continua 171. D.F.AndersonandD.E.Dobbs,Zero-DimensionalCommutativeRings 172. K.Jarosz,FunctionSpaces 173. V.Anconaetal.,ComplexAnalysisandGeometry 174. E.Casas,ControlofPartialDifferentialEquationsandApplications 175. N.Kaltonetal.,InteractionBetweenFunctionalAnalysis,HarmonicAnalysis,andProbability 176. Z.Dengetal.,DifferentialEquationsandControlTheory 177. P.Marcellinietal.PartialDifferentialEquationsandApplications 178. A.Kartsatos,TheoryandApplicationsofNonlinearOperatorsofAccretiveandMonotoneType 179. M.Maruyama,ModuliofVectorBundles 180. A.UrsiniandP.Aglianò,LogicandAlgebra 181. X.H.Caoetal.,Rings,Groups,andAlgebras 182. D.ArnoldandR.M.Rangaswamy,AbelianGroupsandModules 183. S.R.ChakravarthyandA.S.Alfa,Matrix-AnalyticMethodsinStochasticModels 184. J.E.Andersenetal.,GeometryandPhysics 185. P.-J.Cahenetal.,CommutativeRingTheory 186. J.A.Goldsteinetal.,StochasticProcessesandFunctionalAnalysis 187. A.Sorbi,Complexity,Logic,andRecursionTheory 188. G. Da Prato and J.-P. Zolésio, Partial Differential Equation Methods in Control and Shape Analysis 189. D.D.Anderson,FactorizationinIntegralDomains 190. N.L.Johnson,MostlyFiniteGeometries 191. D.HintonandP.W.Schaefer,SpectralTheoryandComputationalMethodsofSturm–Liouville Problems 192. W.H.Schikhofetal.,p-adicFunctionalAnalysis 193. S.Sertöz,AlgebraicGeometry 194. G.CaristiandE.Mitidieri,ReactionDiffusionSystems 195. A.V.Fiacco,MathematicalProgrammingwithDataPerturbations 196. M.Kr'íz''eket al., Finite Element Methods: Superconvergence, Post-Processing, and A PosterioriEstimates 197. S.CaenepeelandA.Verschoren,Rings,HopfAlgebras,andBrauerGroups 198. V.Drenskyetal.,MethodsinRingTheory 199. W.B.JonesandA.SriRanga,OrthogonalFunctions,MomentTheory,andContinuedFractions 200. P.E.Newstead,AlgebraicGeometry 201. D.DikranjanandL.Salce,AbelianGroups,ModuleTheory,andTopology 202. Z.Chenetal.,AdvancesinComputationalMathematics 203. X.CaicedoandC.H.Montenegro,Models,Algebras,andProofs 204. C.Y.Yéldérém andS.A.Stepanov,NumberTheoryandItsApplications 205. D.E.Dobbsetal.,AdvancesinCommutativeRingTheory 206. F.VanOystaeyen,CommutativeAlgebraandAlgebraicGeometry 207. J.Kakoletal.,p-adicFunctionalAnalysis 208. M.BoulagouazandJ.-P.Tignol,AlgebraandNumberTheory 209. S.CaenepeelandF.VanOystaeyen,HopfAlgebrasandQuantumGroups 210. F. Van Oystaeyen and M. Saorin, Interactions Between Ring Theory and Representations of Algebras 211. R.Costaetal.,NonassociativeAlgebraandItsApplications 212. T.-X.He,WaveletAnalysisandMultiresolutionMethods 213. H.HudzikandL.Skrzypczak,FunctionSpaces: TheFifthConference 214. J.Kajiwaraetal.,FiniteorInfiniteDimensionalComplexAnalysis 215. G.LumerandL.Weis,EvolutionEquationsandTheirApplicationsinPhysicalandLifeSciences 216. J.Cagnoletal.,ShapeOptimizationandOptimalDesign 217. J.HerzogandG.Restuccia,GeometricandCombinatorialAspectsofCommutativeAlgebra 218. G.Chenetal.,ControlofNonlinearDistributedParameterSystems 219. F.AliMehmetietal.,PartialDifferentialEquationsonMultistructures 220. D.D.AndersonandI.J.Papick,IdealTheoreticMethodsinCommutativeAlgebra 221. Á.Granjaetal.,RingTheoryandAlgebraicGeometry 222. A.K.Katsarasetal.,p-adicFunctionalAnalysis 223. R.Salvi,TheNavier-StokesEquations 224. F.U.CoelhoandH.A.Merklen,RepresentationsofAlgebras 225. S.AizicoviciandN.H.Pavel,DifferentialEquationsandControlTheory 226. G.Lyubeznik,LocalCohomologyandItsApplications 227. G.DaPratoandL.Tubaro,StochasticPartialDifferentialEquationsandApplications 228. W.A.Carniellietal.,Paraconsistency 229. A.BenkiraneandA.Touzani,PartialDifferentialEquations 230. A.Illanesetal.,ContinuumTheory 231. M.Fontanaetal.,CommutativeRingTheoryandApplications 232. D.MondandM.J.Saia,RealandComplexSingularities 233. V.AnconaandJ.Vaillant,HyperbolicDifferentialOperators AdditionalVolumesinPreparation Preface This volume is based on papers presented at the International Workshop on Differential Equations and Optimal Control, held at the Department of Mathematics of Ohio University in Athens, Ohio. The main objective of this international meeting was to feature new trends in the theory and applications of partial differential and functional-differential equations and their optimal control. The workshop can be viewed as a follow-up to the March 1993 Ohio University International Conference on Optimal Control of Differential Equations, whose proceedings were edited by N. H. Pavel and also published by Marcel Dekker, Inc., as volume 160 of the series: Lecture Note in Pure and Applied Mathematics. A large variety of related topics is covered in this volume, both theoretical and applied, deterministic and stochastic. The topics include: nonlinear programming and control with closed range operators, stabilization of the diffusion equations, flow-invariant sets with respect to the Navier-Stokes equations, numerical approximation of the Riccati equation, telegraph systems, dispersive equations, viable domains for differential equations, almost periodic solutions to neutral functional equations, Wentzell boundary conditions, parabolic phase-field models with memory, Kato classes of distributions, optimal control and algebraic Riccati equations, identification problems for wave equations via optimal control, integrodifferential and other functional equations, stochastic Navier-Stokes equations, Lavrentiev phenomena, volatility for American options via optimal control, obstacle problems, necessary conditions of optimality for semilinear problems, Lyapunov stability, least action for ,/V-body problems, and more. The workshop was sponsored by the College of Arts and Sciences, the Department of Mathematics, and the Research Office of Ohio University. We gratefully acknowledge their financial support, which made this workshop possible. We are also very indebted to all participants and contributors. Finally, our thanks go also to Marcel Dekker, Inc., for undertaking the publication of this volume. Sergiu Aizicovici Nicolae H. Pavel iii