Partial Differential Inequalities with Nonlinear Convolution Terms (SpringerBriefs in Mathematics) - Softcover

Ghergu, Marius

Softcover

ISBN 10: 3031218558 ISBN 13: 9783031218552

Publisher: Springer, 2023

Synopsis

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 presentwork appeals to graduate and postgraduate students as well as to researchers in the field of partial differential equations and nonlinear analysis.

About this title

About the Author

Marius Ghergu earned a PhD in Mathematics at Université de Savoie in France and is currently an Associate Professor in the School of Mathematics and Statistics, University College Dublin, Ireland. He has conducted research and published on nonlinear partial differential equations which model real life phenomena.

From the Back Cover

Edition details

• Publisher: Springer
• Publication date: 2023
• Language: English
• ISBN 10: 3031218558
• ISBN 13: 9783031218552
• Binding: Paperback
• Edition number: 1
• Number of pages: 144