Partial Differential Inequalities with Nonlinear Convolution Terms

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.

• 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.

“This is a very interesting, brief companion book for anyone interested in nonlocal convolutional operators, including weakly nonlocal diffusion operators, and partial differential inequalities. ... the exposition is very well organized with numerous references supplied, many pertaining to further interesting and engaging problems.” (Joseph L. Shomberg, Mathematical Reviews, April, 2025) “This book is a self-contained study of partial differential inequalities with nonlinear convolution terms approached by modern mathematical methods. The motivation of this work is to illustrate how techniques including a priori estimates, Harnack inequalities and integral representation of solutions are used to this type of inequalities … . This book includes in a unitary presentation some author’s original research published in the last few years on the topic … .” (Gabriela Marinoschi, zbMATH 1542.35001, 2024)