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.

Analytic Inequalities And Their Applications In Pdes

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Author : Yuming Qin
language : en
Publisher: Birkhäuser
Release Date : 2017-02-13

Analytic Inequalities And Their Applications In Pdes written by Yuming Qin and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-13 with Mathematics categories.

This book presents a number of analytic inequalities and their applications in partial differential equations. These include integral inequalities, differential inequalities and difference inequalities, which play a crucial role in establishing (uniform) bounds, global existence, large-time behavior, decay rates and blow-up of solutions to various classes of evolutionary differential equations. Summarizing results from a vast number of literature sources such as published papers, preprints and books, it categorizes inequalities in terms of their different properties.

A Priori Estimates And Blow Up Of Solutions To Nonlinear Partial Differential Equations And Inequalities

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Author : Enzo Mitidieri
language : en
Publisher:
Release Date : 2001

A Priori Estimates And Blow Up Of Solutions To Nonlinear Partial Differential Equations And Inequalities written by Enzo Mitidieri and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.

Random Differential Inequalities

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Author : Lakshmikantham
language : en
Publisher: Academic Press
Release Date : 1981-01-13

Random Differential Inequalities written by Lakshmikantham and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-01-13 with Computers categories.

Random Differential Inequalities

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.

Apriori Estimates And Blow Up Of Solutions To Nonlinear Partial Differential Equations And Inequalities

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Author : E. Mitidieri
language : en
Publisher:
Release Date : 2001

Apriori Estimates And Blow Up Of Solutions To Nonlinear Partial Differential Equations And Inequalities written by E. Mitidieri and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.

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.