Описание: For the first time in the mathematical literature, this two-volume work introduces a unified and general approach to the subject. To a large extent, the book is based on the authors` work, and has no significant overlap with other books on the theory of elliptic boundary value problems
Описание: For the first time in the mathematical literature, this two-volume work introduces a unified and general approach to the subject. To a large extent, the book is based on the authors` work, and has no significant overlap with other books on the theory of elliptic boundary value problems.
Описание: The results of this exceptional thesis on free boundary problems in singularly perturbed PDEs develop our understanding of the effects of strong competition between species. The research has a wealth of valuable applications in both physics and biology.
Описание: This new edition incorporates new developments in numerical methods for singularly perturbed differential equations, focusing on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics.
Описание: In addition, it explores the homogenization of hyperbolic partial differential equations with oscillating coefficients and linear oscillatory singularly perturbed hyperbolic partial differential equations.
Описание: This text is about the elimination of fast oscillatory scales in dynamical systems, which is important for efficient computer-simulations and the understanding of model hierarchies. The author presents his method, homogenization in time, based on energy principles and weak convergence techniques.
Описание: In this monograph the authors present detailed and pedagogic proofs of persistence theorems for normally hyperbolic invariant manifolds and their stable and unstable manifolds for classes of perturbations of the NLS equation, as well as for the existence and persistence of fibrations of these invariant manifolds.
Описание: In this monograph the authors present detailed and pedagogic proofs of persistence theorems for normally hyperbolic invariant manifolds and their stable and unstable manifolds for classes of perturbations of the NLS equation, as well as for the existence and persistence of fibrations of these invariant manifolds.
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: 33463.00 р. 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
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.
Описание: Benedict Baur presents modern functional analytic methods for construction and analysis of Feller processes in general and diffusion processes in particular.
Описание: Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. This book offers an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. It can be used as an introductory text to the theory underpinning fitted mesh methods.
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