Emerging concepts in evolution equations /
Emerging concepts in evolution equations /
Carolyn Murphy, editor.
- 1 online resource (viii, 97 pages)
- Mathematics research developments .
- Mathematics research developments series. .
Includes bibliographical references and index.
EMERGING CONCEPTS IN EVOLUTION EQUATIONS ; EMERGING CONCEPTS IN EVOLUTION EQUATIONS ; CONTENTS ; PREFACE; Chapter1THEEVOLUTIONEQUATIONOFLIE-TYPEFORFINITEDEFORMATIONSANDITSTIME-DISCRETEINTEGRATION; Abstract; 1. Introduction; 2. KinematicsofFiniteDeformation; 2.1. LieGroupofTransformations; 2.2. ConfigurationSpaceSym+(N)asaHomogeneousSpace; 2.3. LieAlgebrasgl(N)ando(N)andLieTripleSystemsym(N); 3. EvolutionEquationofLie-typeforFiniteDeformations; 3.1. GeometricalInterpretation; 3.2. SolvingStrategy; 4. EquationofLie-TypeontheLieAlgebra; 4.1. Equation@Ct=DTtCt+CtDt; 4.2. Equation@Ct=2Ut¡DtUt. 4.3. Equation@Ft=LtFt5. Runge-Kutta-Munthe-KaasMethod; 6. MagnusandFerExpansionMethod; 6.1. MagnusExpansionMethod; 6.2. FerExpansionMethod; Conclusion; References; Chapter2NEWAPPLICATIONSOFSYMMETRYANALYSISTONONLINEAREVOLUTIONEQUATIONS; Abstract; 1. Introduction; 2. ContactGroupClassificationofNonlinearEvolutionEquations:Semi-SimpleGroups; 2.1. AdmissibleTransformationsofEvolutionEquations; 2.2. EquationsInvariantunderSemi-SimpleLieAlgebras; 2.3. EquationsInvariantundertheAlgebrasHavingNontrivialLeviFactor; 2.3.1. DirectSumsofSemi-SimpleandSolvableLieAlgebras. 2.3.2. Semi-DirectSumsofSemi-SimpleandSolvableLieAlgebras3. SymmetriesandExactSolutionsoftheTimeFractionalHarry-DymEquationwiththeRiemann-LiouvilleDerivative; 3.1. Preliminaries; 3.2. LieSymmetriesandOptimalSystemfortheFractionalHDEquation; 3.3. SimilarityReductionsoftheFractionalHDEquation; Conclusion; References; Chapter3AMETHODFOREXPONENTIALLYSTABILIZINGACLASSOF1-DPDES; Abstract; 1. FormulationoftheControlProblem; 2. Preliminaries; 2.1ExponentialStabilityinSemigroupsContext; 2.2SystemTransformation; 2.3SemigroupsRepresentationoftheTargetSystem; 3. ExponentialStabilizationoftheTargetSystem. 4. ExponentialStabilizationoftheInitialSystemConclusion; References; INDEX ; Blank Page.
9781536108736 (electronic book) 1536108731 (electronic book) (paperback)
2017001444
Evolution equations.
Evolution equations, Nonlinear.
Differential equations, Partial.
Équations d'évolution.
Équations d'évolution non linéaires.
Équations aux dérivées partielles.
MATHEMATICS--Calculus.
MATHEMATICS--Mathematical Analysis.
Differential equations, Partial.
Evolution equations.
Evolution equations, Nonlinear.
Electronic books.
QA377.3 / .E44 2017
515/.35
Includes bibliographical references and index.
EMERGING CONCEPTS IN EVOLUTION EQUATIONS ; EMERGING CONCEPTS IN EVOLUTION EQUATIONS ; CONTENTS ; PREFACE; Chapter1THEEVOLUTIONEQUATIONOFLIE-TYPEFORFINITEDEFORMATIONSANDITSTIME-DISCRETEINTEGRATION; Abstract; 1. Introduction; 2. KinematicsofFiniteDeformation; 2.1. LieGroupofTransformations; 2.2. ConfigurationSpaceSym+(N)asaHomogeneousSpace; 2.3. LieAlgebrasgl(N)ando(N)andLieTripleSystemsym(N); 3. EvolutionEquationofLie-typeforFiniteDeformations; 3.1. GeometricalInterpretation; 3.2. SolvingStrategy; 4. EquationofLie-TypeontheLieAlgebra; 4.1. Equation@Ct=DTtCt+CtDt; 4.2. Equation@Ct=2Ut¡DtUt. 4.3. Equation@Ft=LtFt5. Runge-Kutta-Munthe-KaasMethod; 6. MagnusandFerExpansionMethod; 6.1. MagnusExpansionMethod; 6.2. FerExpansionMethod; Conclusion; References; Chapter2NEWAPPLICATIONSOFSYMMETRYANALYSISTONONLINEAREVOLUTIONEQUATIONS; Abstract; 1. Introduction; 2. ContactGroupClassificationofNonlinearEvolutionEquations:Semi-SimpleGroups; 2.1. AdmissibleTransformationsofEvolutionEquations; 2.2. EquationsInvariantunderSemi-SimpleLieAlgebras; 2.3. EquationsInvariantundertheAlgebrasHavingNontrivialLeviFactor; 2.3.1. DirectSumsofSemi-SimpleandSolvableLieAlgebras. 2.3.2. Semi-DirectSumsofSemi-SimpleandSolvableLieAlgebras3. SymmetriesandExactSolutionsoftheTimeFractionalHarry-DymEquationwiththeRiemann-LiouvilleDerivative; 3.1. Preliminaries; 3.2. LieSymmetriesandOptimalSystemfortheFractionalHDEquation; 3.3. SimilarityReductionsoftheFractionalHDEquation; Conclusion; References; Chapter3AMETHODFOREXPONENTIALLYSTABILIZINGACLASSOF1-DPDES; Abstract; 1. FormulationoftheControlProblem; 2. Preliminaries; 2.1ExponentialStabilityinSemigroupsContext; 2.2SystemTransformation; 2.3SemigroupsRepresentationoftheTargetSystem; 3. ExponentialStabilizationoftheTargetSystem. 4. ExponentialStabilizationoftheInitialSystemConclusion; References; INDEX ; Blank Page.
9781536108736 (electronic book) 1536108731 (electronic book) (paperback)
2017001444
Evolution equations.
Evolution equations, Nonlinear.
Differential equations, Partial.
Équations d'évolution.
Équations d'évolution non linéaires.
Équations aux dérivées partielles.
MATHEMATICS--Calculus.
MATHEMATICS--Mathematical Analysis.
Differential equations, Partial.
Evolution equations.
Evolution equations, Nonlinear.
Electronic books.
QA377.3 / .E44 2017
515/.35