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Title
Partial differential inequalities with nonlinear convolution terms / Marius Ghergu.
ISBN
9783031218569 (electronic bk.)
3031218566 (electronic bk.)
9783031218552
3031218558
Published
Cham : Springer, 2022.
Language
English
Description
1 online resource (viii, 136 pages) : illustrations.
Other Standard Identifiers
10.1007/978-3-031-21856-9 doi
Call Number
QA374
Dewey Decimal Classification
515/.36
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed January 12, 2023).
Series
SpringerBriefs in mathematics, 2191-8201
Available in Other Form
Print version: 9783031218552
Chapter 1. Preliminary Facts
Chapter 2. Quasilinear Elliptic Inequalities with Convolution Terms
Chapter 3. Singular and Bounded Solutions for Quasilinear Inequalities
Chapter 4. Polyharmonic Inequalities with Convolution Terms
Chapter 5. Quasilinear Parabolic Inequalities with Convolution Terms
Chapter 6. Higher Order Evolution Inequalities with Convolution Terms
Appendix A. Some Properties of Superharmonic Functions
Appendix B. Harnack Inequalities for Quasilinear Elliptic Operators
Bibliography
Index.
