Nonlinear Parabolic Equations and Hyperbolic-Parabolic Coupled Systems, Zheng, Songmu
Автор: Pao, C. V. Название: Nonlinear parabolic and elliptic equations ISBN: 1461363233 ISBN-13(EAN): 9781461363231 Издательство: Springer Рейтинг: Цена: 158380.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: In response to the growing use of reaction diffusion problems in many fields, this monograph gives a systematic treatment of a class of nonlinear parabolic and elliptic differential equations and their applications these problems. It is an important reference for mathematicians and engineers, as well as a practical text for graduate students.
Автор: Gershon Kresin, Vladimir Maz`ya Название: Maximum Principles and Sharp Constants for Solutions of Elliptic and Parabolic Systems ISBN: 0821889818 ISBN-13(EAN): 9780821889817 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 96090.00 T Наличие на складе: Невозможна поставка. Описание: The main goal of this book is to present results pertaining to various versions of the maximum principle for elliptic and parabolic systems of arbitrary order. In particular, the authors present necessary and sufficient conditions for validity of the classical maximum modulus principles for systems of second order and obtain sharp constants in inequalities of Miranda-Agmon type and in many other inequalities of a similar nature. Somewhat related to this topic are explicit formulas for the norms and the essential norms of boundary integral operators. The proofs are based on a unified approach using, on one hand, representations of the norms of matrix-valued integral operators whose target spaces are linear and finite dimensional, and, on the other hand, on solving certain finite dimensional optimization problems. This book reflects results obtained by the authors, and can be useful to research mathematicians and graduate students interested in partial differential equations.
Автор: Ionu? Munteanu Название: Boundary Stabilization of Parabolic Equations ISBN: 3030110982 ISBN-13(EAN): 9783030110987 Издательство: Springer Рейтинг: Цена: 79190.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
This monograph presents a technique, developed by the author, to design asymptotically exponentially stabilizing finite-dimensional boundary proportional-type feedback controllers for nonlinear parabolic-type equations. The potential control applications of this technique are wide ranging in many research areas, such as Newtonian fluid flows modeled by the Navier-Stokes equations; electrically conducted fluid flows; phase separation modeled by the Cahn-Hilliard equations; and deterministic or stochastic semi-linear heat equations arising in biology, chemistry, and population dynamics modeling.
The text provides answers to the following problems, which are of great practical importance:
Designing the feedback law using a minimal set of eigenfunctions of the linear operator obtained from the linearized equation around the target stateDesigning observers for the considered control systemsConstructing time-discrete controllers requiring only partial knowledge of the state
After reviewing standard notations and results in functional analysis, linear algebra, probability theory and PDEs, the author describes his novel stabilization algorithm. He then demonstrates how this abstract model can be applied to stabilization problems involving magnetohydrodynamic equations, stochastic PDEs, nonsteady-states, and more.
Boundary Stabilization of Parabolic Equations will be of particular interest to researchers in control theory and engineers whose work involves systems control. Familiarity with linear algebra, operator theory, functional analysis, partial differential equations, and stochastic partial differential equations is required.
Автор: Atsushi Yagi Название: Abstract Parabolic Evolution Equations and their Applications ISBN: 3642261795 ISBN-13(EAN): 9783642261794 Издательство: Springer Рейтинг: Цена: 102480.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book offers an overview of the theories of linear, semilinear and quasilinear abstract parabolic evolution equations. It also shows how to apply the abstract results to various models in the real world focusing on various self-organization models.
Автор: J?rgen Fuhrmann; Mario Ohlberger; Christian Rohde Название: Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems ISBN: 3319382888 ISBN-13(EAN): 9783319382883 Издательство: Springer Рейтинг: Цена: 111790.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The methods considered in the 7th conference on "Finite Volumes for Complex Applications" (Berlin, June 2014) have properties which offer distinct advantages for a number of applications.
Автор: J?rgen Fuhrmann; Mario Ohlberger; Christian Rohde Название: Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems ISBN: 3319055909 ISBN-13(EAN): 9783319055909 Издательство: Springer Рейтинг: Цена: 149060.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The methods considered in the 7th conference on "Finite Volumes for Complex Applications" (Berlin, June 2014) have properties which offer distinct advantages for a number of applications.
PART 4. Hyperbolic Problems. David Iampietro, Frederic Daude, Pascal Galon, and Jean-Marc Herard, A Weighted Splitting Approach For Low-Mach Number Flows.-
Florence Hubert and Remi Tesson, Weno scheme for transport equation on unstructured grids with a DDFV approach.- M.J. Castro, J.M. Gallardo and A. Marquina, New types of Jacobian-free approximate Riemann solvers for hyperbolic systems.- Charles Demay, Christian Bourdarias, Benoıt de Laage de Meux, Stephane Gerbi and Jean-Marc Herard, A fractional step method to simulate mixed flows in pipes with a compressible two-layer model.- Theo Corot, A second order cell-centered scheme for Lagrangian hydrodynamics.- Clement Colas, Martin Ferrand, Jean-Marc Herard, Erwan Le Coupanec and Xavier Martin, An implicit integral formulation for the modeling of inviscid fluid flows in domains containing obstacles.- Christophe Chalons and Maxime Stauffert, A high-order Discontinuous Galerkin Lagrange Projection scheme for the barotropic Euler equations.- Christophe Chalons, Regis Duvigneau and Camilla Fiorini, Sensitivity analysis for the Euler equations in Lagrangian coordinates.- Jooyoung Hahn, Karol Mikula, Peter Frolkovic, and Branislav Basara, Semi-implicit level set method with inflow-based gradient in a polyhedron mesh.- Thierry Goudon, Julie Llobell and Sebastian Minjeaud, A staggered scheme for the Euler equations.- Christian Bourdarias, Stephane Gerbi and Ralph Lteif, A numerical scheme for the propagation of internal waves in an oceanographic model.- Hamza Boukili and Jean-Marc Herard, A splitting scheme for three-phase flow models.- M. J Castro, C. Escalante and T. Morales de Luna, Modelling and simulation of non-hydrostatic shallow flows.- Svetlana Tokareva and Eleuterio Toro, A flux splitting method for the Baer-Nunziato equations of compressible two-phase flow.- Mohamed Boubekeur and Fayssal Benkhaldoun and Mohammed Seaid, GPU accelerated finite volume methods for three-dimensional shallow water flows.- Ward Melis, Thomas Rey and Giovanni Samaey, Projective integration for nonlinear BGK kinetic equations.- Lei Zhang, Jean-Michel Ghidaglia and Anela Kumbaro, Asymptotic preserving property of a semi-implicit method.- Sebastien Boyaval, A Finite-Volume discretization of viscoelastic Saint-Venant equations for FENE-P fluids.- David Coulette, Emmanuel Franck, Philippe Helluy, Michel Mehrenberger, Laurent Navoret, Palindromic Discontinuous Galerkin Method.- M. Lukacova-Medvid'ova, J. Rosemeier, P. Spichtinger and B. Wiebe, IMEX finite volume methods for cloud simulation.- Raimund Burger and Ilja Kroker, Hybrid stochastic Galerkin finite volumes for the diffusively corrected Lighthill-Whitham-Richards traffic model.- Hamed Zakerzadeh, The RS-IMEX scheme for the rotating shallow water equations with the Coriolis force.- Emmanuel Audusse, Minh Hieu Do, Pascal Omnes, Yohan Penel, Analysis of Apparent Topography scheme for the linear wave equation with Coriolis force.- N. Aıssiouene, M-O. Bristeau, E. Godlewski, A. Mangeney, C. Pares and J. Sainte-Marie, Application of a combined finite element - finite volume method to a 2D non-hydrostatic shallow water problem.- Emanuela Abbate, Angelo Iollo and Gabriella Puppo, A relaxation scheme for the simulation of low Mach number flows.- Stefan Vater, Nicole Beisiegel and Jorn Behrens, Comparison of wetting and drying between a RKDG2 method and classical FV based second-order hydrostatic reconstruction.- Anja Jeschke, Stefan Vater and J]orn Behrens, A Discontinuous Galerkin Method for Non-Hydrostatic Shallow Water Flows.- Remi Abgrall and Paola Bacigaluppi, Design of a Second-Order Fully Explicit Residual Distribution Scheme for Compressible Multiphase Flows.- Martin Campos Pinto, An Unstructured Forward-Backward Lagrangian Scheme for Transport Problems.- Nicole Goutal, Minh-Hoang Le and Philippe Ung, A Godunov-type scheme for Shallow Water equations dedicated to simulations of overland flows on stepped slop
This book is the second volume of proceedings of the 8th conference on "Finite Volumes for Complex Applications" (Lille, June 2017). It includes reviewed contributions reporting successful applications in the fields of fluid dynamics, computational geosciences, structural analysis, nuclear physics, semiconductor theory and other topics.
The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation, and recent decades have brought significant advances in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications.
The book is useful for researchers, PhD and master's level students in numerical analysis, scientific computing and related fields such as partial differential equations, as well as for engineers working in numerical modeling and simulations.
Автор: VIOREL BARBU Название: Controllability and Stabilization of Parabolic Equations ISBN: 3319766651 ISBN-13(EAN): 9783319766652 Издательство: Springer Рейтинг: Цена: 93160.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems.
Автор: N.V. Krylov Название: Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations ISBN: 1470447401 ISBN-13(EAN): 9781470447403 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 107850.00 T Наличие на складе: Невозможна поставка. Описание: This book concentrates on first boundary-value problems for fully nonlinear second-order uniformly elliptic and parabolic equations with discontinuous coefficients. We look for solutions in Sobolev classes, local or global, or for viscosity solutions. Most of the auxiliary results, such as Aleksandrov's elliptic and parabolic estimates, the Krylov-Safonov and the Evans-Krylov theorems, are taken from old sources, and the main results were obtained in the last few years.Presentation of these results is based on a generalization of the Fefferman-Stein theorem, on Fang-Hua Lin's like estimates, and on the so-called ``ersatz'' existence theorems, saying that one can slightly modify ``any'' equation and get a ``cut-off'' equation that has solutions with bounded derivatives. These theorems allow us to prove the solvability in Sobolev classes for equations that are quite far from the ones which are convex or concave with respect to the Hessians of the unknown functions. In studying viscosity solutions, these theorems also allow us to deal with classical approximating solutions, thus avoiding sometimes heavy constructions from the usual theory of viscosity solutions.
Автор: Alexander A. Kovalevsky, Igor I. Skrypnik, Andrey E. Shishkov Название: Singular Solutions of Nonlinear Elliptic and Parabolic Equations ISBN: 3110315483 ISBN-13(EAN): 9783110315486 Издательство: Walter de Gruyter Цена: 223090.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This monograph looks at several trends in the investigation of singular solutions of nonlinear elliptic and parabolic equations. It discusses results on the existence and properties of weak and entropy solutions for elliptic second-order equations and some classes of fourth-order equations with L1-data and questions on the removability of singularities of solutions to elliptic and parabolic second-order equations in divergence form. It looks at localized and nonlocalized singularly peaking boundary regimes for different classes of quasilinear parabolic second- and high-order equations in divergence form.The book will be useful for researchers and post-graduate students that specialize in the field of the theory of partial differential equations and nonlinear analysis.Contents:ForewordPart I: Nonlinear elliptic equations with L^1-dataNonlinear elliptic equations of the second order with L^1-dataNonlinear equations of the fourth order with strengthened coercivity and L^1-dataPart II: Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second orderRemovability of singularities of the solutions of quasilinear elliptic equationsRemovability of singularities of the solutions of quasilinear parabolic equationsQuasilinear elliptic equations with coefficients from the Kato classPart III: Boundary regimes with peaking for quasilinear parabolic equationsEnergy methods for the investigation of localized regimes with peaking for parabolic second-order equationsMethod of functional inequalities in peaking regimes for parabolic equations of higher ordersNonlocalized regimes with singular peakingAppendix: Formulations and proofs of the auxiliary resultsBibliography
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