01342nam a2200361 i 4500991000631879707536041117s2003 sz b 001 0 eng d3764369213b13249605-39ule_instDip.to Matematicaeng332.60151921AMS 90-01AMS 60-01AMS 91-01AMS 91B28AMS 91B30LC HG4515.3.K63Koch Medina, Pablo148629Mathematical finance and probability :a discrete introduction /Pablo Koch Medina, Sandro MerinoBasel ;Boston ;Berlin :Birkhäuser,c2003viii, 328 p. ;25 cmIncludes bibliographical references and indexInvestmentsMathematicsInvestmentsMathematical modelsProbabilitiesSecuritiesMathematical modelsMerino, Sandroauthorhttp://id.loc.gov/vocabulary/relators/aut148630.b1324960502-04-1417-11-04991000631879707536LE013 90-XX KOC11 (2003)12013000149578le013pE45.00-l- 00000.i1395738709-12-04Mathematical finance and probability513732UNISALENTOle01317-11-04ma -engsz 0004083nam 22007455 450 991068679030332120251217160020.09783031245831(electronic bk.)978303124582410.1007/978-3-031-24583-1(MiAaPQ)EBC7221154(Au-PeEL)EBL7221154(OCoLC)1374426207(DE-He213)978-3-031-24583-1(PPN)269093052(CKB)26347443300041(EXLCZ)992634744330004120230328d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierDual Variational Approach to Nonlinear Diffusion Equations /by Gabriela Marinoschi1st ed. 2023.Cham :Springer Nature Switzerland :Imprint: Birkhäuser,2023.1 online resource (223 pages)PNLDE Subseries in Control,2731-7374 ;102Print version: Marinoschi, Gabriela Dual Variational Approach to Nonlinear Diffusion Equations Cham : Springer Basel AG,c2023 9783031245824 Includes bibliographical references and index.Introduction -- Nonlinear Diffusion Equations with Slow and Fast Diffusion -- Weakly Coercive Nonlinear Diffusion Equations -- Nonlinear Diffusion Equations with a Noncoercive Potential -- Nonlinear Parabolic Equations in Divergence Form with Wentzell Boundary Conditions -- A Nonlinear Control Problem in Image Denoising -- An Optimal Control Problem for a Phase Transition Model -- Appendix -- Bibliography -- Index.This monograph explores a dual variational formulation of solutions to nonlinear diffusion equations with general nonlinearities as null minimizers of appropriate energy functionals. The author demonstrates how this method can be utilized as a convenient tool for proving the existence of these solutions when others may fail, such as in cases of evolution equations with nonautonomous operators, with low regular data, or with singular diffusion coefficients. By reducing it to a minimization problem, the original problem is transformed into an optimal control problem with a linear state equation. This procedure simplifies the proof of the existence of minimizers and, in particular, the determination of the first-order conditions of optimality. The dual variational formulation is illustrated in the text with specific diffusion equations that have general nonlinearities provided by potentials having various stronger or weaker properties. These equations can represent mathematical models tovarious real-world physical processes. Inverse problems and optimal control problems are also considered, as this technique is useful in their treatment as well.PNLDE Subseries in Control,2731-7374 ;102Differential equationsSystem theoryControl theoryOperator theoryMathematical optimizationCalculus of variationsDifferential EquationsSystems Theory, ControlOperator TheoryCalculus of Variations and OptimizationEquacions diferencials no linealsthubLlibres electrònicsthubDifferential equations.System theory.Control theory.Operator theory.Mathematical optimization.Calculus of variations.Differential Equations.Systems Theory, Control.Operator Theory.Calculus of Variations and Optimization.Equacions diferencials no lineals260515.355Marinoschi Gabriela517203MiAaPQMiAaPQMiAaPQ9910686790303321Dual Variational Approach to Nonlinear Diffusion Equations3087616UNINA