Shock Formation in Small-Data Solutions to 3D Quasilinear Wave Equations, Jared Speck
Автор: Fuensanta Andreu-Vaillo; Vicent Caselles; Jos? M. Название: Parabolic Quasilinear Equations Minimizing Linear Growth Functionals ISBN: 3034896247 ISBN-13(EAN): 9783034896245 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
This book contains a detailed mathematical analysis of the variational approach to image restoration based on the minimization of the total variation submitted to the constraints given by the image acquisition model. This model, initially introduced by Rudin, Osher, and Fatemi, had a strong influence in the development of variational methods for image denoising and restoration, and pioneered the use of the BV model in image processing. After a full analysis of the model, the minimizing total variation flow is studied under different boundary conditions, and its main qualitative properties are exhibited. In particular, several explicit solutions of the denoising problem are computed.
Автор: Pr?ss Название: Moving Interfaces and Quasilinear Parabolic Evolution Equations ISBN: 3319276972 ISBN-13(EAN): 9783319276977 Издательство: Springer Рейтинг: Цена: 121110.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis.The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions, and an exposition of the geometry of moving hypersurfaces.
Автор: Fuensanta Andreu-Vaillo; Vicent Caselles; Jos? M. Название: Parabolic Quasilinear Equations Minimizing Linear Growth Functionals ISBN: 3764366192 ISBN-13(EAN): 9783764366193 Издательство: Springer Рейтинг: Цена: 93130.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Details the mathematical developments in total variation based image restauration. This book is devoted to PDE`s of elliptic and parabolic type associated to functionals having a linear growth in the gradient, with a special emphasis on the applications related to image restoration and nonlinear filters.
Автор: Herbert Amann Название: Linear and Quasilinear Parabolic Problems ISBN: 3034899505 ISBN-13(EAN): 9783034899505 Издательство: Springer Рейтинг: Цена: 130430.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This distinguishes it from the theory of nonlinear contraction semigroups whose basis is a nonlinear version of the Hille- Yosida theorem: the Crandall-Liggett theorem. Thus the theory of nonlinear contraction semigroups does not apply to systems, in general, since they do not allow for a maximum principle.
Название: Global Solutions And The Asymptotic Behavior For Nonlinear Wave Equations With Small Initial Data ISBN: 4864970548 ISBN-13(EAN): 9784864970549 Издательство: World Scientific Publishing Цена: 44350.00 T Наличие на складе: Невозможна поставка. Описание: In the study of the Cauchy problem for nonlinear wave equations with small initial data, the case where the nonlinearity has the critical power is of special interest. In this case, depending on the structure of the nonlinearity, one may observe global existence and finite time blow-up of solutions. In 80's, Klainerman introduced a sufficient condition, called the null condition, for the small data global existence in the critical case. Recently, weaker sufficient conditions are also studied.This volume offers a comprehensive survey of the theory of nonlinear wave equations, including the classical local existence theorem, the global existence in the supercritical case, the finite time blow-up and the lifespan estimate in the critical case, and the global existence under the null condition in two and three space dimensions. The main tool here is the so-called vector field method. This volume also contains recent progress in the small data global existence under some conditions weaker than the null condition, and it is shown that a wide variety of the asymptotic behavior is observed under such weaker conditions.This volume is written not only for researchers, but also for graduate students who are interested in nonlinear wave equations. The exposition is intended to be self-contained and a complete proof is given for each theorem.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets
This book is devoted to the study of elliptic second-order degenerate quasilinear equations, the model of which is the p-Laplacian, with or without dominant lower order reaction term. Emphasis is put on three aspects:
The existence of separable singular solutions enables the description of isolated singularities of general solutions. The construction of singular solutions is delicate and cannot be done without the understanding of the spherical p-harmonic eigenvalue problem.
When the equations are considered on a Riemannian manifold, existence or non-existence of solutions depends on geometric assumptions such as the curvature. A priori estimates and Liouville type problems are analyzed.
When the equations are considered with a forcing term in the class of measures, their study is strongly linked to the properties of a class of potentials appearing in harmonic analysis such as the Riesz, the Bessel or the Wolff potentials and to their associated capacities. Necessary and sufficient conditions for existence of solutions link the continuity of the measure with respect to some appropriate capacity.
Автор: Alexander Koshelev Название: Regularity Problem for Quasilinear Elliptic and Parabolic Systems ISBN: 3540602518 ISBN-13(EAN): 9783540602514 Издательство: Springer Рейтинг: Цена: 41880.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This text deals with regular or strong solutions for general quasilinear second-order elliptic and parabolic systems. Applications in solid mechanics, hydrodynamics, elasticity and plasticity are described.
Автор: Sharma, Vishnu D. Название: Quasilinear Hyperbolic Systems, Compressible Flows, and Waves ISBN: 0367384159 ISBN-13(EAN): 9780367384159 Издательство: Taylor&Francis Рейтинг: Цена: 65320.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
Filled with practical examples, Quasilinear Hyperbolic Systems, Compressible Flows, and Waves presents a self-contained discussion of quasilinear hyperbolic equations and systems with applications. It emphasizes nonlinear theory and introduces some of the most active research in the field.
After linking continuum mechanics and quasilinear partial differential equations, the book discusses the scalar conservation laws and hyperbolic systems in two independent variables. Using the method of characteristics and singular surface theory, the author then presents the evolutionary behavior of weak and mild discontinuities in a quasilinear hyperbolic system. He also explains how to apply weakly nonlinear geometrical optics in nonequilibrium and stratified gas flows and demonstrates the power, generality, and elegance of group theoretic methods for solving Euler equations of gasdynamics involving shocks. The final chapter deals with the kinematics of a shock of arbitrary strength in three dimensions.
With a focus on physical applications, this text takes readers on a journey through this fascinating area of applied mathematics. It provides the essential mathematical concepts and techniques to understand the phenomena from a theoretical standpoint and to solve a variety of physical problems.
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