Partial Differential Inequalities With Nonlinear Convolution Terms

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Partial Differential Inequalities With Nonlinear Convolution Terms

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Author : Marius Ghergu
language : en
Publisher:
Release Date : 2022

Partial Differential Inequalities With Nonlinear Convolution Terms written by Marius Ghergu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Differential equations categories.

This brief research monograph uses modern mathematical methods to investigate partial differential equations with nonlinear convolution terms, enabling readers to understand the concept of a solution and its asymptotic behavior. In their full generality, these inequalities display a non-local structure. Classical methods, such as maximum principle or sub- and super-solution methods, do not apply to this context. This work discusses partial differential inequalities (instead of differential equations) for which there is no variational setting. This current work brings forward other methods that prove to be useful in understanding the concept of a solution and its asymptotic behavior related to partial differential inequalities with nonlinear convolution terms. It promotes and illustrates the use of a priori estimates, Harnack inequalities, and integral representation of solutions. One of the first monographs on this rapidly expanding field, the present work appeals to graduate and postgraduate students as well as to researchers in the field of partial differential equations and nonlinear analysis.

Partial Differential Inequalities With Nonlinear Convolution Terms

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Author : Marius Ghergu
language : en
Publisher: Springer Nature
Release Date : 2023-01-01

Partial Differential Inequalities With Nonlinear Convolution Terms written by Marius Ghergu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Mathematics categories.

This brief research monograph uses modern mathematical methods to investigate partial differential equations with nonlinear convolution terms, enabling readers to understand the concept of a solution and its asymptotic behavior. In their full generality, these inequalities display a non-local structure. Classical methods, such as maximum principle or sub- and super-solution methods, do not apply to this context. This work discusses partial differential inequalities (instead of differential equations) for which there is no variational setting. This current work brings forward other methods that prove to be useful in understanding the concept of a solution and its asymptotic behavior related to partial differential inequalities with nonlinear convolution terms. It promotes and illustrates the use of a priori estimates, Harnack inequalities, and integral representation of solutions. One of the first monographs on this rapidly expanding field, the present work appeals to graduate and postgraduate students as well as to researchers in the field of partial differential equations and nonlinear analysis.

Nonlinear Partial Differential Equations

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Author : Mi-Ho Giga
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-30

Nonlinear Partial Differential Equations written by Mi-Ho Giga 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 2010-05-30 with Mathematics categories.

This work will serve as an excellent first course in modern analysis. The main focus is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. This textbook will be an excellent resource for self-study or classroom use.

Perspectives In Partial Differential Equations Harmonic Analysis And Applications

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Author : Dorina Mitrea
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Perspectives In Partial Differential Equations Harmonic Analysis And Applications written by Dorina Mitrea 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 2008 with Mathematics categories.

This volume contains a collection of papers contributed on the occasion of Mazya's 70th birthday by a distinguished group of experts of international stature in the fields of harmonic analysis, partial differential equations, function theory, and spectral analysis, reflecting the state of the art in these areas.

Fourier Analysis And Nonlinear Partial Differential Equations

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Author : Hajer Bahouri
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-03

Fourier Analysis And Nonlinear Partial Differential Equations written by Hajer Bahouri 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 2011-01-03 with Mathematics categories.

In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those techniques based on the Littlewood-Paley decomposition have proved to be very efficient for the study of evolution equations. The present book aims at presenting self-contained, state- of- the- art models of those techniques with applications to different classes of partial differential equations: transport, heat, wave and Schrödinger equations. It also offers more sophisticated models originating from fluid mechanics (in particular the incompressible and compressible Navier-Stokes equations) or general relativity. It is either directed to anyone with a good undergraduate level of knowledge in analysis or useful for experts who are eager to know the benefit that one might gain from Fourier analysis when dealing with nonlinear partial differential equations.

Harnack Inequalities And Nonlinear Operators

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Author : Vincenzo Vespri
language : en
Publisher: Springer Nature
Release Date : 2021-05-29

Harnack Inequalities And Nonlinear Operators written by Vincenzo Vespri and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-29 with Mathematics categories.

The book contains two contributions about the work of Emmanuele DiBenedetto and a selection of original papers. The authors are some of the main experts in Harnack’s inequalities and nonlinear operators. These papers are part of the contributions presented during the conference to celebrate the 70th birthday of Prof. Emmanuele DiBenedetto, which was held at “Il Palazzone” in Cortona from June 18th to 24th, 2017. The papers are focused on current research topics regarding the qualitative properties of solutions, connections with calculus of variations, Harnack inequality and regularity theory. Some papers are also related to various applications. Many of the authors have shared with Prof. DiBenedetto an intense scientific and personal collaboration, while many others have taken inspiration from and further developed his field of research. The topics of the conference are certainly of great interest for the international mathematical community.

Nonlinear Analysis Differential Equations And Control

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Author : F.H. Clarke
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Nonlinear Analysis Differential Equations And Control written by F.H. Clarke 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.

Recent years have witnessed important developments in those areas of the mathematical sciences where the basic model under study is a dynamical system such as a differential equation or control process. Many of these recent advances were made possible by parallel developments in nonlinear and nonsmooth analysis. The latter subjects, in general terms, encompass differential analysis and optimization theory in the absence of traditional linearity, convexity or smoothness assumptions. In the last three decades it has become increasingly recognized that nonlinear and nonsmooth behavior is naturally present and prevalent in dynamical models, and is therefore significant theoretically. This point of view has guided us in the organizational aspects of this ASI. Our goals were twofold: We intended to achieve "cross fertilization" between mathematicians who were working in a diverse range of problem areas, but who all shared an interest in nonlinear and nonsmooth analysis. More importantly, it was our goal to expose a young international audience (mainly graduate students and recent Ph. D. 's) to these important subjects. In that regard, there were heavy pedagogical demands placed upon the twelve speakers of the ASI, in meeting the needs of such a gathering. The talks, while exposing current areas of research activity, were required to be as introductory and comprehensive as possible. It is our belief that these goals were achieved, and that these proceedings bear this out. Each of the twelve speakers presented a mini-course of four or five hours duration.

The Maz Ya Anniversary Collection

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Author : Jürgen Rossmann
language : en
Publisher: Springer Science & Business Media
Release Date : 1999

The Maz Ya Anniversary Collection written by Jürgen Rossmann 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 1999 with Differential equations, Partial categories.

Probabilistic Models For Nonlinear Partial Differential Equations

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Author : Carl Graham
language : en
Publisher: Springer
Release Date : 2006-11-13

Probabilistic Models For Nonlinear Partial Differential Equations written by Carl Graham and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-13 with Mathematics categories.

The lecture courses of the CIME Summer School on Probabilistic Models for Nonlinear PDE's and their Numerical Applications (April 1995) had a three-fold emphasis: first, on the weak convergence of stochastic integrals; second, on the probabilistic interpretation and the particle approximation of equations coming from Physics (conservation laws, Boltzmann-like and Navier-Stokes equations); third, on the modelling of networks by interacting particle systems. This book, collecting the notes of these courses, will be useful to probabilists working on stochastic particle methods and on the approximation of SPDEs, in particular, to PhD students and young researchers.

Partial Differential Equations And Applications

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Author : Giorgio Talenti
language : en
Publisher: Routledge
Release Date : 2017-10-02

Partial Differential Equations And Applications written by Giorgio Talenti and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-02 with Mathematics categories.

Written as a tribute to the mathematician Carlo Pucci on the occasion of his 70th birthday, this is a collection of authoritative contributions from over 45 internationally acclaimed experts in the field of partial differential equations. Papers discuss a variety of topics such as problems where a partial differential equation is coupled with unfavourable boundary or initial conditions, and boundary value problems for partial differential equations of elliptic type.