Singularities Of Solutions Of Second Order Quasilinear Equations

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Singularities Of Solutions Of Second Order Quasilinear Equations

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Author : Laurent Veron
language : en
Publisher: CRC Press
Release Date : 1996-08-01

Singularities Of Solutions Of Second Order Quasilinear Equations written by Laurent Veron and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-08-01 with Mathematics categories.

This text examines the singularity problem for solutions of elliptic and parabolic quasilinear equations of second order.

Singular Solutions Of Nonlinear Elliptic And Parabolic Equations

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Author : Alexander A. Kovalevsky
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-03-21

Singular Solutions Of Nonlinear Elliptic And Parabolic Equations written by Alexander A. Kovalevsky and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-21 with Mathematics categories.

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: Foreword Part I: Nonlinear elliptic equations with L^1-data Nonlinear elliptic equations of the second order with L^1-data Nonlinear equations of the fourth order with strengthened coercivity and L^1-data Part II: Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second order Removability of singularities of the solutions of quasilinear elliptic equations Removability of singularities of the solutions of quasilinear parabolic equations Quasilinear elliptic equations with coefficients from the Kato class Part III: Boundary regimes with peaking for quasilinear parabolic equations Energy methods for the investigation of localized regimes with peaking for parabolic second-order equations Method of functional inequalities in peaking regimes for parabolic equations of higher orders Nonlocalized regimes with singular peaking Appendix: Formulations and proofs of the auxiliary results Bibliography

Elliptic Boundary Value Problems Of Second Order In Piecewise Smooth Domains

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Author : Michail Borsuk
language : en
Publisher: Elsevier
Release Date : 2006-01-12

Elliptic Boundary Value Problems Of Second Order In Piecewise Smooth Domains written by Michail Borsuk and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-12 with Mathematics categories.

The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. The authors concentrate on the following fundamental results: sharp estimates for strong and weak solutions, solvability of the boundary value problems, regularity assertions for solutions near singular points.Key features:* New the Hardy – Friedrichs – Wirtinger type inequalities as well as new integral inequalities related to the Cauchy problem for a differential equation.* Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.* The question about the influence of the coefficients smoothness on the regularity of solutions.* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.* The behaviour of weak solutions near conical point for the Dirichlet problem for m – Laplacian.* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.* Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.* The question about the influence of the coefficients smoothness on the regularity of solutions.* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.* The behaviour of weak solutions near conical point for the Dirichlet problem for m - Laplacian.* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.

Local And Global Aspects Of Quasilinear Degenerate Elliptic Equations Quasilinear Elliptic Singular Problems

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Author : Laurent Veron
language : en
Publisher: World Scientific
Release Date : 2017-05-05

Local And Global Aspects Of Quasilinear Degenerate Elliptic Equations Quasilinear Elliptic Singular Problems written by Laurent Veron and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-05 with Mathematics categories.

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:

Nonlinear Second Order Elliptic Equations Involving Measures

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Author : Moshe Marcus
language : en
Publisher: Walter de Gruyter
Release Date : 2013-11-27

Nonlinear Second Order Elliptic Equations Involving Measures written by Moshe Marcus and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.

In the last 40 years semi-linear elliptic equations became a central subject of study in the theory of nonlinear partial differential equations. On the one hand, the interest in this area is of a theoretical nature, due to its deep relations to other branches of mathematics, especially linear and nonlinear harmonic analysis, dynamical systems, differential geometry and probability. On the other hand, this study is of interest because of its applications. Equations of this type come up in various areas such as problems of physics and astrophysics, curvature problems in Riemannian geometry, logistic problems related for instance to population models and, most importantly, the study of branching processes and superdiffusions in the theory of probability. The aim of this book is to present a comprehensive study of boundary value problems for linear and semi-linear second order elliptic equations with measure data. We are particularly interested in semi-linear equations with absorption. The interactions between the diffusion operator and the absorption term give rise to a large class of nonlinear phenomena in the study of which singularities and boundary trace play a central role. This book is accessible to graduate students and researchers with a background in real analysis and partial differential equations.

Nonlinear Diffusion Equations And Their Equilibrium States 3

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Author : N.G Lloyd
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Nonlinear Diffusion Equations And Their Equilibrium States 3 written by N.G Lloyd and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Nonlinear diffusion equations have held a prominent place in the theory of partial differential equations, both for the challenging and deep math ematical questions posed by such equations and the important role they play in many areas of science and technology. Examples of current inter est are biological and chemical pattern formation, semiconductor design, environmental problems such as solute transport in groundwater flow, phase transitions and combustion theory. Central to the theory is the equation Ut = ~cp(U) + f(u). Here ~ denotes the n-dimensional Laplacian, cp and f are given functions and the solution is defined on some domain n x [0, T] in space-time. FUn damental questions concern the existence, uniqueness and regularity of so lutions, the existence of interfaces or free boundaries, the question as to whether or not the solution can be continued for all time, the asymptotic behavior, both in time and space, and the development of singularities, for instance when the solution ceases to exist after finite time, either through extinction or through blow up.

Classical And Quantic Periodic Motions Of Multiply Polarized Spin Particles

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Author : Abbas Bahri
language : en
Publisher: CRC Press
Release Date : 1997-11-28

Classical And Quantic Periodic Motions Of Multiply Polarized Spin Particles written by Abbas Bahri and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-11-28 with Mathematics categories.

:The author of this volume defines a diffusion flow for a variational problem lacking completeness related to the geometry of a contact form a a and a vector field u in its kernel. He analyzes the ends of the flow lines and finds them to be of two types: one involving periodic orbits of the Reeb (Hamiltonian) vector field x, and the other where asymptotes occur. In the most general case these turn out to be periodic motions for x up to quantic jumps of a very special type along u. He shows that the mathematical results and the physical interpretation fit and provide new points of view useful in the foundations of quantum mechanics.

Numerical Analysis 1997

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Author : D.F. Griffiths
language : en
Publisher: CRC Press
Release Date : 1997-12-05

Numerical Analysis 1997 written by D.F. Griffiths and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-12-05 with Mathematics categories.

This book forms a valuable guide to the direction in which current numerical analysis research is heading. It will be of particular interest to graduate students and researchers concerned with the theoretical and practical issues associated with scientific computation. The main topics include ordinary and partial differential equations, fluid flow, optimization, linear algebra, and approximation theory. Two recurring themes are the need for adaptive and structure preserving numerical methods. The work presented here has a list of direct applications that include colliding black holes, molecular dynamics, blow-up problems, and card shuffling.

A Complete Classification Of The Isolated Singularities For Nonlinear Elliptic Equations With Inverse Square Potentials

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Author : Florica C. Cîrstea
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-01-08

A Complete Classification Of The Isolated Singularities For Nonlinear Elliptic Equations With Inverse Square Potentials written by Florica C. Cîrstea and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-08 with Mathematics categories.

In particular, for b = 1 and λ = 0, we find a sharp condition on h such that the origin is a removable singularity for all non-negative solutions of [[eqref]]one, thus addressing an open question of Vázquez and Véron.

Integral Methods In Science And Engineering

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Author : Christian Constanda
language : en
Publisher: CRC Press
Release Date : 2020-03-31

Integral Methods In Science And Engineering written by Christian Constanda and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-31 with Mathematics categories.

Based on proceedings of the International Conference on Integral Methods in Science and Engineering, this collection of papers addresses the solution of mathematical problems by integral methods in conjunction with approximation schemes from various physical domains. Topics and applications include: wavelet expansions, reaction-diffusion systems, variational methods , fracture theory, boundary value problems at resonance, micromechanics, fluid mechanics, combustion problems, nonlinear problems, elasticity theory, and plates and shells. Volume 1 covers Analytic Methods.