Emerging concepts in evolution equations /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Otros Autores: Murphy, Carolyn (Writer on mathematics) (Editor )
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York : Nova Science Publishers, Inc., [2017]
Colección:Mathematics research developments series.
Temas:
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.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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